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=62​, find the probability of a sample mean being less than 22.6 if μ=23 and sigmaσ=1.18 is?

Answer 1

solution

mean =   = 23

standard deviation = = 1.18

n = 62

= 23

=  / n = 1.18/ 62 = 0.15

P( < 22.6) = P[( - ) / < (22.6-23) /0.15 ]

= P(z <-2.67 )

Using z table  

= 0.0038   

probability= 0.0038