A population of values has a normal distribution with μ=231.3and σ=64. You intend to draw a random sample of size n=247. Find the probability that a sample of size n=247n=247 is randomly selected with a mean between 230.1 and 233.7. P(230.1 < ¯X¯ < 233.7) = Round to 4 decimal places.

A population of values has a normal distribution with μ=231.3and σ=64. You intend to draw a random sample of size n=247. Find the probability that a sample of size n=247n=247 is randomly selected with a mean between 230.1 and 233.7. P(230.1 < ¯X¯ < 233.7) = Round to 4 decimal places.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 8E

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Question

A population of values has a normal distribution with μ=231.3and σ=64. You intend to draw a random sample of size n=247.

Find the probability that a sample of size n=247n=247 is randomly selected with a mean between 230.1 and 233.7.
P(230.1 < ¯X¯ < 233.7) = Round to 4 decimal places.

Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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