(1 point)
The number of eggs that a female house fly lays during her lifetime is normally distributed with mean 790 and standard deviation 92.
Random samples of size 98 are drawn from this population, and the mean of each sample is determined. What is the probability that
the mean number of eggs laid would differ from 790 by less than 30? Round your answer to four decimal places.

Answer:

0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Mean 790 and standard deviation 92.

This means that [tex]\mu = 790, \sigma = 92[/tex]

Samples of 98

This means that [tex]n = 98, s = \frac{92}{\sqrt{98}}[/tex]

What is the probability that the mean number of eggs laid would differ from 790 by less than 30?

This is the pvalue of Z when X = 790 + 30 = 820 subtracted by the pvalue of Z when X = 790 - 30 = 760. So

X = 820

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{820 - 790}{\frac{92}{\sqrt{98}}}[/tex]

[tex]Z = 3.23[/tex]

[tex]Z = 3.23[/tex] has a pvalue of 0.9994

X = 760

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{760 - 790}{\frac{92}{\sqrt{98}}}[/tex]

[tex]Z = -3.23[/tex]

[tex]Z = -3.23[/tex] has a pvalue of 0.0006

0.9994 - 0.0006 = 0.9988

0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.

Quadrilateral CDEF is similar to quadrilateral GHIJ. Find the measure of side IJ. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.

Thank you:)

Answer please !! Due in 45 minutes m

Hey, can someone please help me with this? I don’t know how to solve it.
Thank you.

I need help with is one. Thank you so much!

PLEASE NO DOWNLOADS AND PLEASE ANSWER IT QUICK

Describe the transformation shown in the graph

The angle measurements in the diagram are represented by the following expressions;

Use the matrix tool to solve the system of equations. Choose the correct
ordered pair.
4x - 7y = -5
-6x+ 5y = 2
PLEASE HELP

Find the missing term in the
geometric sequence.
13,[ ? 1,208

Help Plzzzzzzzzzzzzzzzzzzz

What is the following simplified product? Assume x >0.
(Square root 6x^2 + 4 square root 8x^3) ( Square root 9X - x square 5x^5)?

A point is shown on the coordinate plane below. Where is the point located? *

Which graph represents the equation y = - 4/3 x - 2 ?

Pls help meeeee thank you

WILL NAME BRAINLIST PLEASE
Use the table to write a linear function that relates y to x . PLEASE NO HACKERS
y=

monika has 3 1/4 cups of rice. each sushi roll she makes required 7/16 of cup of rice to make with the rice she has how many full sushi rolls can monika make​

HELP ILL GIVE BRAINLIEST AND NO LINKS

please help and I think the answer is c.​

How do I solve this? I need help

Trents family has 28 pears and will eat 4 per day

ABCD ~ QRST
Find the missing side length, m.
B
10 C
Rms
13
12
15
5.2 4.8
6
ST
9
A
22.5
D
m = [?]

15% of customers that come to your
taco truck order two tacos. If 300 guests
come to your store, how many of them
will you expect to order two tacos?
NO LINKS

2- Describe the cross section

help plz plz plz ill give brain​

3(x-4)^2=27 solution

a customer purchases windows for $15,000 using a credit card. If the interest is compounded monthly at a rate of 16% per year, how much interest will be charged at the end of three years?​

Please help, how many terms are in the expression?

Create an expression equivalent to 4(3x+2y)

Find the area of the parallelogram:
35 ft
A
24 ft
30 ft
Label your answer.
The area of the parallelogram is

1. 3, 4
2. odd number, even number
3. 5, 5
4. odd number, odd number
5. 2, 3
6. 1, 3
7. 7, 1