A random sample is drawn from a normally distributed population with mean μ = 31 and standard deviation σ = 1.9. Calculate the probabilities that the sample mean is less than 31.6 for both sample sizes

For sample size n = 39 ; P(X < 31.6) = 0.9756

For sample size n = 76 ; P(X < 31.6) = 0.9970

Step-by-step explanation:

Given that:

population mean μ = 31

standard deviation σ = 1.9

sample mean   = 31.6

Sample size n                 Probability

39

76

The probabilities that the sample mean is less than 31.6 for both sample size can be computed as  follows:

For sample size n = 39

From standard normal  tables

P(X < 31.6) = 0.9756

For sample size n = 76

From standard normal  tables

P(X < 31.6) = 0.9970