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=6565​, find the probability of a sample mean being greater than 219 if muμequals=218 and sigmaσequals=5.8

For a sample of n=65​, the probability of a sample mean being greater than 219 if μ=218 and sigmaσequals=5.8 is?

Answer 1

n = 65

μ = 218

σ = 5.8 / √65 = 0.7194

X = 219

Z = X - μ / σ

Z = 219 -218 / 0.7194

Z = 1.39

P(x >219)

=p( z > 1.39)

= 0.5 - 0.4177 [standard normal distribution table]

= 0.0823 or 8.23%

The sample mean does not considered unusual because probabality is greater than 0.05 of the sample mean within the range.