it is expected that 35% of students in a math course offered at northern university will earn an a. using excel to approximate the binomial distribution with a normal distribution, find the probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn an a.
Answers
The probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn is 0.9998..
We have given that,
A data of students in a math course offered at northern university will earn .
Total number of randomly selected students enrolled in the course = 300
i.e total number of trials, n = 300
probability of success, p = 35% = 0.35
probability of failure, q = 1-0.35 = 0.65
np = 300× 0.35 =
n(1-p) = 300×0.65 =
both np and n(1-p) are greater than 10 , so we can use normal approximation here.
We have to calculate probability that more than 75 of them will earn an , P(X>75). Using Binomial Probability distribution, X~ Bin(300, 0.35)
P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾
Now, P(X>75) = 1 - P(X=<75)
but here data is large, that is n= 300, x = 75 so tough to calculate it by hands , thus we use Excel function to find out the required probability. Excel Command: =BINOM.DIST(number_s,trials,probability_s,cumulative)
where, Number_s (required argument) -->the number of successes in trials,i.e "x" Trials (required argument) --> the number of independent trials i.e , "n" must 0≤ n. Probability_s (required argument) --> the probability of success in each trial.
Cumulative (required argument)-->A logical value that determines the form of the function. It can either be: TRUE--> Uses the cumulative distribution function and FALSE--> Uses the probability mass function. Now, for P(X ≤ 75) , the function is look like as
=BINOM.DIST(75,300, 0.35, TRUE) =0.000126081
=BINOM.DIST(75,300, 0.35, FALSE)
= 5.0305E-05
Now, the required probability, P(X> 75)
= 1 - P(X ≤75)
= 1 - 5.03095E-05 = 0.999949691
or using cumulative distribution function,
P(X>75) = 0.999873919
both are give approx. same results
.So, required probability is 0.9998.
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Related Questions
one and three fifths plus three and two thirds equals blank
Answers
Answer:
5 [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
1 [tex]\frac{3}{5}[/tex] = 8/5
3 [tex]\frac{2}{3}[/tex] = 11/3
In order to add fractions, the denominators, or the bottom numbers, have to be the same. To make them the same, find the common denominator (the lowest number that both the numbers can be divisible by)
8/5+ 11/3 the common denominator would be 15 so multiply the appropriate numbers to the denominators and the numerators (the top number)
24/15 + 55/15 = 79/15
Now simplify
79/15 = 5 [tex]\frac{4}{15}[/tex]
Two marbles are chosen at random, one at a time from a box that contains 7 marbles, 5 red and 2 green, a. Find the probability of drawing 2 red marbles when
Answers
The probability of randomly drawing 2 red marbles is P = 0.476
How to find the probability?On the box we have 7 marbles, 5 red ones and 2 green ones. If we assume all the marbles have the same probability of being randomly drawn, then the probability of drawing a red marble is equal to the quotient between the number of red marbles and the total number of marbles.
So the probability for the first red marble is:
p = 5/7
For the second one, we will have one red marble less and one marble of the total less, so the probability is:
q = 4/6
The joint probability is the product of these two:
P = (5/7)*(4/6) = 0.476
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In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=11 and BC=6, what is the area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your answer.
Answers
Answer:
The area of the shaded region is 36.
In rectangle ABCD, point E lies halfway between sides AB and CD and halfway between sides AD and BC. This means that line segment AE is parallel to line segment CD and is half as long, and line segment BE is parallel to line segment AD and is also half as long.
Since AE is half as long as CD, and CD is twice as long as AE, we can say that CD is equal to 2 * AE. Similarly, since BE is half as long as AD, and AD is twice as long as BE, we can say that AD is equal to 2 * BE.
Since AD is equal to 2 * BE and CD is equal to 2 * AE, the lengths of AD and CD are equal. This means that the shaded region is a parallelogram with sides of equal length.
The area of a parallelogram is equal to the product of its base and height. In this case, the base of the parallelogram is 6 (the length of side BC) and the height is AE + BE (the combined length of the two sides of the parallelogram).
We know that AE is half as long as CD, and CD is twice as long as AE, so CD is equal to 2 * AE. Since CD is equal to 2 * AE, AE is equal to CD / 2. Since CD is equal to 11 (the length of side AB), AE is equal to 11 / 2 = 5.5.
Similarly, we know that BE is half as long as AD, and AD is twice as long as BE, so AD is equal to 2 * BE. Since AD is equal to 2 * BE, BE is equal to AD / 2. Since AD is equal to 6 (the length of side BC), BE is equal to 6 / 2 = 3.
The combined length of AE and BE is 5.5 + 3
Sara needs to determine the number of 3/4 pound servings into 9 3/4 pounds of turkey.she calculates that there are 13 servings.is stated calculation correct why or why not
Answers
There are 9.75 servings, not 13 servings.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
the number of 3/4 pound servings in pounds of turkey
she calculates that there are 13 servings.
so,
9 (3/4) = (36 + 3) /4
= 39/4
= 9.75
Hence, there are 9.75 servings, not 13 servings.
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A semi-circle has an area of 50 m². Find the perimeter of the semi-circle. Give your answer correct to one decimal place.
Answers
Answer:
29.0 m
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4cm}\underline{Area of a semicircle}\\\\$A=\dfrac{1}{2}\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius\\ \end{minipage}}[/tex]
Given the area of the semicircle is 50 m², substitute this into the formula and rearrange to isolate r:
[tex]\begin{aligned}\implies\dfrac{1}{2}\pi r^2&=50\\\pi r^2 & = 100\\r^2 & = \dfrac{100}{\pi}\\r&=\sqrt{\dfrac{100}{\pi}}\end{aligned}[/tex]
The perimeter of a semicircle is the sum of the diameter of the circle and half its circumference.
Diameter of a circle = 2rCircumference of a circle = 2πrTherefore:
[tex]\begin{aligned}\textsf{Perimeter of a semicircle}&=2r+\pi r\\&=r(2+\pi)\\&=\sqrt{\dfrac{100}{\pi}}(2+\pi)\\&=29.0083301...\end{aligned}[/tex]
Therefore, the perimeter of the semicircle is 29.0 m (1 d.p.).
The distance around a circular park is 88 yards.
What is the area of the park? Use 3.14 for π.
Answers
Answer:
616.25 [tex]yd^2[/tex]
Step-by-step explanation:
The equation for the area of a circle is
[tex]A=\pi r^2[/tex]
Since the problem does not give a value for r, it must be derived. Recall that the equation for the circumference of a circle is
[tex]C=2\pi r[/tex]
Using the given value of the circumference,
[tex]C=88yd=2\pi r[/tex]
So,
[tex]88yd=2\pi r\\\frac{88yd}{2\pi}=r\\14.01yd=r[/tex]
Insert the derived value of r into the formula for area:
[tex]A=\pi r^2\\A=\pi(14.01yd)^2\\A=616.25yd^2[/tex]
Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 99% confidence and Researcher 2 wants to estimate with 95% confidence. Which researcher would need more students for her study in order to obtain the desired margin of error? Researcher 1 Researcher 2 Both researchers would need the same number of subjects. OIt is impossible to obtain the same margin of error with the two different confidence levels.
Answers
The researcher who needs more students for her study in order to obtain the desired margin of error would be: Researcher 1. The correct answer is the first option.
Researcher 1 needs more students for her study in order to obtain the desired margin of error, because she wants to estimate with 99% confidence, while Researcher 2 wants to estimate with 95% confidence.
What is the relation between margin of error and level of confidence?The margin of error and the level of confidence are connected together. A better margin of error may be resulted for a lesser level of confidence, or a higher level of confidence may be obtained by tolerating a larger margin of error.
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Each marble bag sold by Jane's Marble Company contains 4 purple marbles for every 5 red marbles. If a bag has 24 purple
marbles, how many red marbles does it contain?
Answers
The no: of red marbles, that the bag contains if it has 24 purple marbles are 30 marbles.
What is a unitary in math?a single state. This has an identity element in math, in an algebra. Whose inverse is equivalent to its adjoint (in mathematics, linear algebra, mathematical study of a matrix or operator).
What is unitary formula?The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What is the unitary rule?A unitary government is a type of government in which the whole government is controlled by a single entity, known as the central government. Actually, the center of authority for all administrative divisions and powers.
In the given question,
for every 4 purple marbles there are 5 red marbles
then for 1 purple marble there is 5/4 red marbles
again for 24 purple marbles, there are 30 red marbles
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the manager of a bank record of the amount of each Time customer spent waiting in the line during peak business hours on Monday the waiting times are shown below find the mean waiting time Roger answer to one Decimal place 6.8 min 7.5 min 7.2 min brainly
Answers
What is 7,899 to the nearest thousand
Answers
Answer: 8,000
Step-by-step explanation: So, to find how to round this to the nearest 1000, we need to look at the 3 digits being the 7. So, 899 is greater than 500, so we round up, so 7 + 1 is 8, and we change those 3 digits behind the zero to 0's, so we get 8,000. I hoped this helped.
Answer:
8000
7899 rounded to nearest thousand is 8000, because 7 is in thousand's place value, and the number after that is 8, which is more than 5, so 1 is added to 7, and it becomes 8. The rest of the numbers turn to 0.
so you get 8000.
hope it helps :)
Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Use a significance level of α = 0.01
Sample 1: n1 = 13, ¯x1 = 23, s1 = 6
Sample 2: n2 = 16, ¯x2 = 29, s2 = 5.9
(a) The degree of freedom is _____
(b) The test statistic is _____
(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0
(d) |t| > _____
Answers
To test the claim that the two samples described come from populations with the same mean, we can use a two-sample t-test.
(a) The degree of freedom is 27
(b) The test statistic is -2.67
(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0 : we do not reject the null hypothesis.
(d) |t| > 2.70
(1) The degree of freedom for the two-sample t-test is calculated as
df = n1 + n2 - 2 = 13 + 16 - 2 = 27.(2) The test statistic for the two-sample t-test is calculated as:
t = (¯x1 - ¯x2) / sqrt[(s1^2 / n1) + (s2^2 / n2)]Plugging in the values, we get:
t = (23 - 29) / sqrt[(6^2 / 13) + (5.9^2 / 16)] = -6 / sqrt[(36/13) + (34.81/16)] = -6 / sqrt[2.77 + 2.18] = -6 / sqrt[4.95] = -6 / 2.23 = -2.67(3) To determine the rejection region for the test, we can use a significance level of α = 0.01. For a two-tailed test with α = 0.01, the critical value for t is approximately 2.70. Since our test statistic (-2.67) is less than the critical value, we do not reject the null hypothesis.
(4) For the rejection region, we need to consider values of t that are either greater than or less than the critical value. Therefore, we need to consider |t| values that are greater than 2.70. |t| > 2.70.
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Copy and complete the equation of line G below
y=___x+____
Answers
Answer:
y = 3x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (1, 7) ← 2 points on the line
m = [tex]\frac{7-4}{1-0}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 3x + 4 ← equation of line
find the measure of m< YBA
Answers
The measure of an angle m ∠YBA=47°.
What is meant by an angle?In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.
Since,
ΔFBA=ΔYBA
The two triangles in the provided illustration are comparable.
So,
From the figure:
m ∠FBA=47°
So, m ∠YBA=47°
Therefore, the measure of angle m ∠YBA=47°
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an online magazine allows you to view up to 25 articles free to view 30articles, you pay $49.15. to view 33 articles, you pay $57.40. what is the cost of each article for which you pay a fee?
Answers
Answer:
$2.75
Step-by-step explanation:
The difference in cost for 33 articles and 30 articles is
$57.40 - $49.15 = $8.25
From 30 to 33 articles, the difference is 3 articles.
3 articles cost $8.25.
Cost per article = $8.25/3 = $2.75
Nine less than two times a number is five more than this number. What is the number?
Answers
Answer:
14
Step-by-step explanation:
let n be the number then 2 times the number is 2n and so
2n - 9 = n + 5 ( subtract n from both sides )
n - 9 = 5 ( add 9 to both sides )
n = 14
then the required number is 14
HELP URGENT
A set of data items is normally distributed with a mean of 200 and a standard deviation of 40. Find the data item in this
distribution that corresponds to the given z-score.
z = -3
The data item that corresponds to z = -3 is ___
(Type an integer or a decimal.)
Answers
Answer:
the data item that corresponds to z = -3 is 80.
Step-by-step explanation:
Question 2 of 10
Which statement regarding salaried employees is true?
A. Salaried employees get paid more for additional hours worked.
B. Salaried employees have taxes with held from each paycheck.
c. Salaried employees do not receive an agreed-upon annual pay.
D. Salaried employees never receive medical benefits.
Answers
I looked it up
Answer the question below and for part B write the equation with the answer that you get for part A.
A
B
C
D
Answers
From the linear function, the rate of change is 35 and the unit cost is 35
Linear FunctionA linear function is defined as a function that has either one or two variables without exponents.
In this problem, we have to write a linear function that models the table given. This will take the form of y = mx + c
m = slope or rate of change and c = constant or unit cost of the product.
The formula of slope of a line is given as
m = y₂ - y₁ / x₂ - x₁
Taking two points from the table;
m = 215 - 180 / 5 - 4
m = 35
Using the slope of the line, we can find the y - intercept of the function.
y = mx + c
215 = 35(5) + c
215 = 175 + c
c = 215 - 175
c = 40
The linear function of the table is y = 35x + 40
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DUE SOON!! PLEASE HELP SO CONFUSED!!!!
ITS DUE IN AN HOUR!
Answers
Answer:
Step-by-step explanation:
Write an inequality that represents the sentence:
14 fewer than a number is at least -8.
and
the product of a number and 5 is no more than 8.
Answers
2. 5x <= 8
help Me out and I’ll give you brainliest
Answers
Answer: 5/8
Step-by-step explanation: There are 8 members. Out of 8, there are 5 people's weight that are higher than 135. Therefore the answer is 5/8.
Is the weight of a bike a function of how old it is?
Answers
The weight of an object is the amount of the gravitation pull of the Earth on the object. No, the weight of a bike is not a function of its age.
What i weight?The mass of an object is the quantity of matter it contains, while the weight is the amount of gravitational pull of the Earth on the object. Thus the greater the mass of an object is, the greater its weight. This implies that the weight of an object can be influenced by its value of mass.
The mass of an object can be determined or measured by the use of any of the weighing balances, while the weight of an object can be measured by the use of any of the spring balances. Therefore, the answer to the given question is NO. The weight of a bike is NOT a function of its age. The weight of the bike will depend on the number, and weight of its component parts.
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is 0 a solution for w+3=w
Answers
Answer:No
Step-by-step explanation:
0+3 = 3, not zero
[tex]5^{2} -2^{2} =[/tex]
Answers
5^2 - 2^2 = 21
(5*5) - (2*2)
25 - 4
21
A bus station runs a shuttle service to and from the airport. A shuttle that left the station traveling at 39 miles per hour is passed by a second shuttle that left 30 minutes later traveling at a rate of 42 miles per hour. How far did the first shuttle travel before it was passed by the second shuttle?
Answers
To find the distance that the first shuttle traveled before it was passed by the second shuttle, we need to use the formula d = rt, where d is the distance traveled, r is the speed at which the shuttle is traveling, and t is the time elapsed. We can use this formula to find the distance traveled by each shuttle and then subtract the distance traveled by the first shuttle from the distance traveled by the second shuttle to find the distance the first shuttle traveled before it was passed.
For the first shuttle, the speed is 39 miles per hour and the time elapsed is 30 minutes. Since there are 60 minutes in an hour, the time elapsed in hours is 30 minutes / 60 minutes/hour = 0.5 hours. So, the distance traveled by the first shuttle is 39 miles/hour * 0.5 hours = 19.5 miles.
For the second shuttle, the speed is 42 miles per hour and the time elapsed is 30 minutes. Since there are 60 minutes in an hour, the time elapsed in hours is 30 minutes / 60 minutes/hour = 0.5 hours. So, the distance traveled by the second shuttle is 42 miles/hour * 0.5 hours = 21 miles.
Therefore, the distance that the first shuttle traveled before it was passed by the second shuttle is 21 miles - 19.5 miles = 1.5 miles.
Date Exchange Rate
October 8, 1982 267.38 Yen = 1 US dollar
June 30, 1995 84.90 Yen = 1 US dollar
a. Determine the cost, in US dollars, for a souvenir that cost 3,500 Yen
on October 8, 1982. Show your work in the provided space.
Answers
Using proportions, the value of 3500 Yen on October 8, 1982 is 13.1 USD
ProportionsProportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
On October 8, 1982;
267.38 Yen = 1US
The cost of 3500 Yen = ?
267.38 Yen = 1 USD
35000 Yen = x USD
Cross multiply both sides and solve for x
x * 267.38 = 3500 * 1
267.38x = 3500
Divide both sides by coefficient of x
267.38x / 267.38 = 3500 / 267.38
x = 13.1
The value of 3500 Yen is 13.1 USD
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pls i need it now
thx i might gv brainliest
Answers
The total pay that Nelly will get for last week is £220.
What will the total pay of Nelly be ?From the information given, the following can be deduced:
£8 per hour for the first 15 hours
£10 let hour for any extra hour.
The above are applicable for Monday to Friday.
£16 is the rate for Saturdays.
The number of hours that Nelly worked from Monday to Friday will be:
= 3 1/2 + 5 + 2 1/2 + 4 + 2
= 17 hours
On Saturday, he worked 5 hours.
The total earnings will be:
= (£8 × 15) + (£10 × 2) + (£16 × 5)
= £120 + £20 + £80
= £220
The total amount is £220.
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Sarah received 23 chromosomes from her mother and 23 chromosomes from her father. The combination of genes on these chromosomes code for proteins that express her traits. Choose the words or phrases to complete the sentence. A diagram of a Punnett square. The top of the Punnett square is labeled Father with x and y above the boxes. The side of the square is labeled Mother with x and x on the left side of the boxes. The top row, first box has xx female, the top row, second box has xy male. The second row, first box has xx female, the second row, second box has xy male. There are two long, tubular object along the side of the diagram labeled x chromosome. There is a small circular object on the bottom of the diagram labeled y chromosome. The chromosomes in the image are called Choose... , and the chances of being born male or female are Choose... .
Answers
The chromosomes in the image are called sex chromosomes, and the chances of being born male or female are 1:1.
What is a chromosome?In Science, a chromosome can be defined as a thread-like linear strand of deoxyribonucleic acid (DNA) that is typically found in the nucleus of each cell in a living organism.
What are the characteristics of a chromosome?In Genetics, some of the characteristics of a chromosome include the following:
Chromosomes are made up of a long deoxyribonucleic acid (DNA) molecule that is tightly wound.Every chromosome consist of many genes with each gene being a single segment of deoxyribonucleic acid (DNA).Furthermore, the human somatic cell primarily comprises 46 chromosomes which are normally sub-divided into 23 pairs of chromosomes with 22 of these pairs being autosomes and a pair of sex chromosomes (X and Y).
In this context, we can reasonably infer and logically deduce that the x and y chromosomes are generally referred to as sex chromosomes.
Since Sarah received 23 chromosomes each from her mother and father, the chances of being born male or female is given by;
Ratio = 23: 23.
Dividing both sides by 23, we have;
Ratio = 1:1.
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is (y+3) a factor of the polynomial: y^3-6y+9
Answers
(y + 3) is not a factor of the polynomial y^3-6y+9.
Define polynomial.A polynomial is an equation made up of terms, exponents, constants, variables (or indeterminate values), and variables. The polynomial 3x2 -2x-10 is an illustration. Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Given,
Polynomial
y³ - 6y + 9
(y+3) as a factor
(y + 3) (y+3)
y² + 3y + 3y + 9
y² + 6y + 9
(y + 3) is not a factor of the polynomial: y^3-6y+9.
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cos 0 = 0.8192 A = 45
H = ?
Answers
The value of H (Hypotenuse) will be 54.93
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The values are,
⇒ cos θ = 0.8192
⇒ A (Base) = 45
Now,
Since, The values are,
⇒ cos θ = 0.8192
⇒ A = 45
We know that;
⇒ cos θ = Base (A) / Hypotenuse (H)
Substitute all the values, we get;
⇒ 0.8192 = 45 / H
⇒ H = 45 / 0.8192
⇒ H = 54.93
Thus, The value of H (Hypotenuse) = 54.93
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