Question

A population of values has a normal distribution with μ=89.5μ=89.5 and σ=22.5σ=22.5. You intend to draw a random sample of size n=210n=210. Please show your answers as numbers accurate to 4 decimal places.

Find the probability that a single randomly selected value is between 91.1 and 92.
P(91.1 < X < 92) =

Find the probability that a sample of size n=210n=210 is randomly selected with a mean between 91.1 and 92.
P(91.1 < ¯xx¯ < 92) =

Answer 1

Given that, mean (μ) = 89.5 and standard deviation = 22.5

a) We want to find, P(91.1 < X < 92)

=>P(91.1 < X < 92) = 0.0159

b) sample size (n) = 210

We want to find,