A population of values has a normal distribution with μ = 135.9 and o= 53.8. You intend to draw a random sample of size n = 165. Find the probability that a single randomly selected value is greater than 140.9. P(X> 140.9) = Find the probability that a sample of size n = 165 is randomly selected with a mean greater than 140.9. P(M> 140.9) = 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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A population of values has a normal distribution with μ = 135.9 and σ = 53.8. You intend to draw a random
sample of size n = 165.
Find the probability that a single randomly selected value is greater than 140.9.
P(X > 140.9) =
Find the probability that a sample of size n = 165 is randomly selected with a mean greater than 140.9.
P(M> 140.9) =
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.
Transcribed Image Text:A population of values has a normal distribution with μ = 135.9 and σ = 53.8. You intend to draw a random sample of size n = 165. Find the probability that a single randomly selected value is greater than 140.9. P(X > 140.9) = Find the probability that a sample of size n = 165 is randomly selected with a mean greater than 140.9. P(M> 140.9) = 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.
Expert Solution
Step 1: Determine the given data

From the provided information,

mu equals 135.9
sigma equals 53.8
n equals 165
X tilde N space left parenthesis 135.9 comma 53.8 right parenthesis


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