A population of values has a normal distribution with μ=137.3μ=137.3 and σ=11.3σ=11.3. You intend to draw a random sample of size n=226n=226. Find the probability that a single randomly selected value is between 136.2 and 138.1. P(136.2 < X < 138.1) =  Find the probability that a sample of size n=226n=226 is randomly selected with a mean between 136.2 and 138.1. P(136.2 < M < 138.1) =  Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

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 53E
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A population of values has a normal distribution with μ=137.3μ=137.3 and σ=11.3σ=11.3. You intend to draw a random sample of size n=226n=226.

Find the probability that a single randomly selected value is between 136.2 and 138.1.
P(136.2 < X < 138.1) = 

Find the probability that a sample of size n=226n=226 is randomly selected with a mean between 136.2 and 138.1.
P(136.2 < M < 138.1) = 

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

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