) Study cited that the calcium levels in men and women ages 70 years or older are summarized that sample size of 55 men with mean 785 and standard deviation 489 and sample size of 40 women with mean 670 and standard deviation of 419, what is the probability of obtaining a difference between sample means of 110 mg or more?
Answer:
0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the central limit theorem and difference between normal variables.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal sample means:
When we subtract two distribution of the sample means, which are normal, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of standard errors squared.
Sample size of 55 men with mean 785 and standard deviation 489
This means that:
[tex]\mu_A = 785[/tex]
[tex]s_A = \frac{489}{\sqrt{55}} = 65.9367[/tex]
Sample size of 40 women with mean 670 and standard deviation of 419
This means that:
[tex]\mu_B = 670[/tex]
[tex]s_B = \frac{419}{\sqrt{40}} = 66.2497[/tex]
Difference between sample means:
The mean and the standard deviation are, respectively:
[tex]\mu = \mu_A - \mu_B = 785 - 670 = 115[/tex]
[tex]\sigma = \sqrt{s_A^2+s_B^2} = \sqrt{65.9367^2+66.2497^2} = 93.47[/tex]
What is the probability of obtaining a difference between sample means of 110 mg or more?
This is 1 subtracted by the pvalue of Z when X = 110. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 115}{93.47}[/tex]
[tex]Z = -0.053[/tex]
[tex]Z = -0.053[/tex] has a pvalue of 0.4812.
1 - 0.4812 = 0.5188
0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more
In a school 156 student passed Geography or History There were 75 student who passed in both subject If 9 more passed Geography than History Find how many were taking each subject
Answer:I’m not sure but I thinks it’s b might be wrong
Step-by-step explanation:
In the figure below, m2 1=(x-12)° and mZ2 =5xº.
Find the angle measures.
Answer:
15 165
Step-by-step explanation:
m1 + m2 = 180
x-18 +5x = 180
6x = 198
x = 33
m1 = 15
m2 = 165
Mohamed spent $40 buying three pizzas do you order the wings roommates. Each pizza cost twice as much as the wings +1 dollar. What does one order of wings cost
Answer:
26
Step-by-step explanation:
PLEASE HELP ME FAST!!!!!!!!!!!!
Answer:
c
Step-by-step explanation:
what is the answer to this?
Answer:
i can only say that you should use this forumla, the sins law
sin(a)/A = sin(b)/B = sin(c)/C
Step-by-step explanation:
for triangle ABC with sides a,b and c the law of cosines states
c^2=
in which of the following cases must the law of cosines be used to solve a triangle?
ASA SSS SAS SSA
Option C is correct. The law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)
For a triangle, ABC with sides a, b, and c respectively, the law of cosines is used on such a triangle if there is a presence of an angle between any two sides.
For example, if angle C is between the sides a and b, the equivalent cosine rule will be expressed as:[tex]c^2 = a^2 + b^2 + 2ab cos C[/tex]
Hence the law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)
Learn more here: https://brainly.com/question/20880990
. Three employees each clocked a different number of hours worked this week.
Employee Hours Worked Total Earned (in dollars)
A 35 $420
B 22 $242
C 16 $216
Which employee has the highest earnings per hour?
A) Employee A
B) Employee B
C) Employee C
Answer:
C IS THE ANSWER
A circle is centered on point B. Points A, C and D lie on its circumference.
If ZADC measures 62°, what does ZABC measure?
Answer:
122
Step-by-step explanation:
61 x 2 = 122 hope this helps:)
Guys please tell me the answer
Answer:
from 10 - 15 bikes
Step-by-step explanation:
if the square is directly proportional to w and z =4 when w =8
Answer:
when you calculate the value of w is z= 5
Step-by-step explanation:
Use the inequalities to answer the following question
Inequality 1: 2x + 7 < -3
Inequality 2: x – 8 + 3x < -4
Which of the following values make both inequalities TRUE? Select all that apply.
A.) 12
B.) 325
C.) –10
D.) 2/3
E.) –8.25
F.) -15/2
G.)–5
Answer:
C, E, and F
Explanation:
There are two ways to answer this question. First, you could simply input each answer into both equations to see which one works but that would take quite a long time.
A better way is to simply solve each equation for x.
You could rewrite
2x + 7 < -3
as
2x + 7 = -3
and solve:
Subtract 7 from both sides
[tex](2x + 7) -7 = (-3) - 7\\2x = -10[/tex]
Now divide both sides by 2
[tex]\frac{2x}{2} = \frac{-10}{2}\\x = -5[/tex]
Now we can simply replace the equals sign with the inequality
x < -5
Where you can run into trouble is if you have to multiply or divide by a negative number across the equation, you must flip the inequality sign. It's best to leave it there to remind you, but I switched it out just to show that it's no different than a typical algebraic equation.
Now, we know that x can be any value less than -5. Let's find out the same thing for the second equation:
[tex]x - 8 + 3x < -4\\(x + 3x) -8 < -4\\4x - 8 < -4\\(4x - 8) + 8 < (-4) + 8\\4x < 4\\\frac{4x}{4} < \frac{4}{4}\\x < 1[/tex]
Now we know that x must be less than 1 for the second equation. So, now we can choose the answers that are both less than -5 and less than 1.
These answers are:
C. -10
E. -8.24
and
F. -15/2 which is -7.5
NOTE: -5 is equal to but not less than -5 so G is not included.
A density graph for all of the possible temperatures from 60 degrees to 160 degrees can be used to find which of the following?
A.The probability of a temperature from 30 degrees to 120 degrees
B.The probability of a temperature from 90 degrees to 180 degrees
C.The probability of a temperature from 30 degrees to 90 degrees
D.The probability of a temperature from 90 degrees to 120 degrees
Answer: 90 degrees to 120
Step-by-step explanation:
The probability of a temperature from 90 degrees to 120 degrees.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Experiment: A trial or an operation conducted to produce an outcome is called an experiment.
Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.
Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).
Trial: A trial denotes doing a random experiment.
Given:
Temperatures from 60 degrees to 160 degrees.
As, per the situation the probability will lie between 60 degree to 160 degree.
Hence, The probability of a temperature from 90 degrees to 120 degrees.
Learn more about probability here:
https://brainly.com/question/11234923
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Consider the following data representing the price of laptop computers (in dollars). 1465, 1151, 1344, 1200, 1468, 1310, 1177, 1220, 1148, 1347, 1404, 1405, 1313, 1289, 1431, 1136, 1335, 1160, 1387, 1219, 1329 Price of Laptop Computers (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency 1132–1191 1192–1251 1252–1311 1312–1371 1372–1431 1432–1491 Step 3 of 7 : Determine the lower class boundary for the sixth class.
Solution :
Class Frequency Class boundaries Mid Relative Cumulative
point frequency frequency
1132-1191 5 1131.5-1191.5 1161.5 0.2381 5
1192-1251 3 1191.5-1251.5 1221.5 0.1428 8
1252-1311 2 1251.5-1311.5 1281.5 0.0952 10
1312-1371 5 1311.5-1371.5 1341.5 0.2381 15
1371-1431 4 1371.5-1431.5 1401.5 0.1905 19
1432-1491 2 1431.5-1491.5 1416.5 0.0952 21
Total 21
Therefore, the lower class boundary for the sixth class is 1431.5
Answer:
21
Step-by-step explanation:
1132-1191 5 1131.5-1191.5 1161.5 0.2381 5
1192-1251 3 1191.5-1251.5 1221.5 0.1428 8
1252-1311 2 1251.5-1311.5 1281.5 0.0952 10
1312-1371 5 1311.5-1371.5 1341.5 0.2381 15
1371-1431 4 1371.5-1431.5 1401.5 0.1905 19
1432-1491 2 1431.5-1491.5 1416.5 0.0952 21
please say i'm right
Can someone please help me with this question
Answer:
volume= 186ft
Step-by-step explanation:
The base area of a rectangular prism is 56 square feet. If the height of the prism is 3 feet, what is the total volume of the prism (in cubic feet)?
Ambrosone et al. (2004) conducted an observational study to explore whether broccoli consumption reduces the risk of developing breast cancer in premenopausal women. They report a p-value of 0.058. PROPOSITION ONE: The results suggest a statistically significant association between broccoli consumption and reduced risk of breast cancer at the 5% significance level; PROPOSITION TWO: The results prove the null hypothesis at the 5% significance level.
a. PROPOSITION ONE is true and PROPOSITION TWO is true
b. PROPOSITION ONE is true and PROPOSITION TWO is false
c. PROPOSITION ONE is false and PROPOSITION TWO is true
d. PROPOSITION ONE is false and PROPOSITION TWO is false
e. None of the above
Answer:
c. PROPOSITION ONE is false and PROPOSITION TWO is true
Step-by-step explanation:
In this question, we have that:
pvalue of 0.058
Significance level of 0.05
The pvalue is larger than the significance level, which means that there is no statistically significant association(Propostion One is false), and the null hypothesis is not rejected, that is, it is proved, so Proposition Two is true.
This means that the correct answer is given by option C.
Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 45 expectant mothers have mean weight increase of 16.3 pounds in the second trimester, with a standard deviation of 5.9 pounds. A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds. Find the p -value for the hypothesis test. The p -value should be rounded to 4 decimal places.
Answer:
0.9955
Step-by-step explanation:
Given :
Mean weight increase , μ = 14
Sample mean weight increase , xbar = 16.3
Standard deviation, s = 5.9
Sample size, n = 45
Hypothesis :
H0 : μ = 14
H1 : μ > 14
The test statistic : (xbar - μ) ÷ (s/sqrt(n))
Test statistic = (16.3 - 14) ÷ (5.9/sqrt(45))
Test statistic = 2.3 / 0.8795200
Test statistic = 2.615
The Pvalue :
P(Z < 2.615) = 0.99554
Hence, pvalue = 0.9955 (4 decimal places).
Using the distributive property, what would be the expression (I DONT NEED ANSWER) 1/4(8 + x + 4).
Answer:x/4+3
Step-by-step explanation:
8/1×1/4=8/4=2
X/1×1/4=x/4
4/1×1/4=1
Answer:
2 + [tex]\frac{1}{4} x[/tex] + 1
Step-by-step explanation:
The numbers of licensed drivers in four samples taken from a population of
students are shown in the table below. Which of the following choices is most
likely closest to the percentage of students in the population who are
licensed drivers?
Sample Size Number of Licensed Drivers
25
7
50
12
75
15
100
16
O A. 16%
O B. 20%
ОООО
C. 24%
O D. 28%
Answer:
The answer is 16% I just took the test
Step-by-step explanation:
find the area of this parallelogram. no links just give the answer plz.
Answer:98
Step-by-step explanation:
because it is a rectangle at a slight angle so base * height
Brainlest plz
1/3 (4 ∙ 3) + 23
I need help
Answer:
27
But tell me the exact question it has on there
Step-by-step explanation:
2cosθ−2=0
please type here and not put in a file
Answer:
Step-by-step explanation:
You want the value of theta, I take it. Add 2 to both sides
2cos(theta) = 2 Divide by 2
2cos(theta)/2 = 2/2
cos(theta) = 1
So theta = 0 degrees.
So 0,360 .... n*360 is the general solution.
What is the difference of
7/8 − 1/3
Answer:
[tex]13 \div 24[/tex]
13/24
Step-by-step explanation:
[tex]7 \div 8 - 1 \div 3[/tex]
[tex]taking \: the \: lcm \: of \: 8 \: and \: 3[/tex]
[tex]21 - 8 \div 24[/tex]
[tex]13 \div 24[/tex]
if it helps don't forget to like and mark me
The difference between two positive integers is 4. If the smaller is added to the square of the larger, the sum is 52. Find the integers.
Answer:
The integers are 7 and 3
Step-by-step explanation:
if you put x as smaller number and y as bigger number you can write two equations:
x+y^2=52 and y-4=x
In the first polynomial, y can either equal 7 or -8, but the number has to be positive, so it's 7
y-4 to get x, plug 7 in and you get x=3
y=7 and x=3
Answer:
7 and 3
Step-by-step explanation:
We will let x equal the larger one
y will be the smaller one
We can write the two equations
x-y=4
y+x²=52
We will solve this through substitution
we will take the first equation and add y to moth sides
x=4+y
we then substitute this into our second equation
y+(4+y)²=52
distribute the square
y+8y+y²+16=52
y²+9y-36=0
Factor this
(y-3)(y+12)=0
Which means that y is either 3 or -12 but because it said that both numbers are positive we can reject the negative 12 (which means that y is 3)
Plug in y=3 into our first equation
x-3=4
x=7
there's 20 points for both problems if you could please solve this
What is the mean absolute deviation of the following set of data?
4,6,12,8,10,10,7,8
Two numbers total 58 and have a difference of 8 . Find the two numbers.
Answer:
x = 33 , y = 25
Here's your solution
=> let both number be x and y
=> so, x + y = 58
=> x - y = 8
=> solving both equation { add both }
=> 2x = 66
=> x = 33
=> now putting value of x in equation
=> 33 + y = 58
=> y = 58 - 33
=> y = 25
hope it helps
Prisha is buying sandwiches at a café for herself and her daughter. If she buys 2 tuna sandwiches, the cost will be $14. If she buys 1 tuna sandwich and 1 chicken sandwich, the cost will be $16. How much will the cost be if she buys 2 chicken sandwiches?
Answer:
18$
Step-by-step explanation:
2 tuna sandwiches= 14$
1 tuna sandwich= 14÷2 = 7$
1 tuna sandwich + 1 chicken sandwich = 16$
7$ +1 cs= 16$
1 chicken sandwich = 16$- 7$
1 chicken sandwich = 9$
2 chicken sandwiches = 9x2 = 18$
Your weekly allowance is $15. You spent 30% How much did you spend?
Answer:
You would have spent $4.50
Step-by-step explanation: Divide 100 by 30 and multiply to 15. So it will look like: 30/100*15= $4.50. I hope this helps