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 nequals65​, find the probability of a sample mean being greater than 229 if muequals228 and sigmaequals3.5.

Answer 1

Solution :

Given that ,

mean = = 228

standard deviation = = 3.5

n = 65

= 228

= / n = 3.5 / 65 = 0.43

P( >229 ) = 1 - P( < 229)

= 1 - P[( - ) / < (229-228) / 0.43]

= 1 - P(z < 2.33)

Using z table,    

= 1 - 0.9901

probability= 0.0099