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 =70, find the probability of a sample mean being greater than 226 if μ=225 and sigma =5.8

Answer 1

Solution :

Given that ,

mean = = 225

standard deviation = = 5.8

= / n = 5.8 / 70 = 0.6932

P( > 226) = 1 - P( < 226)

= 1 - P[( - ) / < (226 - 225) / 0.6932]

= 1 - P(z < 1.44)

= 1 - 0.9251

= 0.0749

Probability = 0.0749

It is  unusual because probability not  unusual > 0.05