Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n equals 66​, find the probability of a sample mean being less than 20.6 if mu equals 21 and sigma equals 1.16. LOADING... Click the icon to view page 1 of the standard normal table. LOADING... Click the icon to view page 2 of the standard normal table. For a sample of n equals 66​, the probability of a sample mean being less than 20.6 if mu equals 21 and sigma equals1.16 is

Answer 1

Here, μ = 21, σ = 0.1429and x = 20.6. We need to compute P(X <= 20.6). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (20.6 - 21)/0.1429 = -2.8

Therefore,
P(X <= 20.6) = P(z <= (20.6 - 21)/0.1429)
= P(z <= -2.8)
= 0.0026

yes, the given sample mean would be considered unusual