Answer to Question #209986 in Statistics and Probability for nena

Question #209986

A sample of size 60 is taken from a population of chocolate balls. The weights of chocolate

balls are normally distributed with a mean of 40 g and a standard deviation of 8 g.

a. Find the parameters for this distribution of the sample mean.

b. Find the probability that the sample mean is between 38 g and 42


1
Expert's answer
2021-06-24T09:09:33-0400

Let "\\bar{X}=" the sample mean: "\\bar{X}\\sim N(\\mu, \\sigma^2\/n)."

a.


"\\mu_{\\bar{X}}=\\mu=40\\ g, \\sigma_{\\bar{X}}=\\sigma\/\\sqrt{n}=8\/\\sqrt{60}\\ g"

b.


"P(38<\\bar{X}<42)=P(\\bar{X}<42)-P(\\bar{X}\\leq38)"

"=P(Z<\\dfrac{42-40}{8\/\\sqrt{60}})-P(Z\\leq\\dfrac{38-40}{8\/\\sqrt{60}})"

"\\approx P(Z<1.93649)-P(Z\\leq-1.93649)""\\approx 0.973596-0.026404\\approx0.9472"

The probability that the sample mean is between 38 g and 42 g is 0.9472.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS