A sample of n=25 scores is selected from a normal population with μ = 100 and...

A sample of n=25 scores is selected from a normal population with μ = 100 and σ = 20 .

a. What is the probability that the sample mean will be greater than 120?

b. What is the probability that the sample mean will be less than 105?

c. What is the p (90 < M < 110)?

Solutions

Expert Solution

z score for normal distribution formula

z = (M - μ) / (σ / sqrt(n))

a. What is the probability that the sample mean will be greater than 120?

z = (120 - 100) / (20/sqrt(25)) = 5

P(Z > 5) = 0

The probability that the sample mean will be greater than 120 = 0

b. What is the probability that the sample mean will be less than 105?

z = (105 - 100) / (20/sqrt(25)) =1

P(Z < 1) = 0.8413

c. What is the p (90 < M < 110)?

z = (90 - 100) / (20/sqrt(25)) = -3

z = (110 - 100) / (20/sqrt(25)) = 3

p (90 < M < 110) = 0.9973

orchestra answered 1 year ago

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