Question

The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If​ convenient, use technology to find the probability. For a sample of n equals 32​, find the probability of a sample mean being less than 12,751 or greater than 12,754 when mu equals 12,751 and sigma equals 1.1.

Answer 1

Solution :

Given that,

mean = = 12751

standard deviation = = 1.1

n = 32

= = 12751

= / n = 1.1 / 32 = 0.194

P(12751 < < 12754)  

= P[(12751 - 12751) / 0.194 < ( - ) / < (12754 - 12751) / 0.194 )]

= P(0 < Z < 15.46)

= P(Z < 15.46 ) - P(Z < 0)

Using z table,  

= 1 - 0.5

= 0.5

No, it would be not unusual because probability more than 5%