Question

In: Statistics and Probability

The population mean and standard deviation are given below. Find the indicated probability and determine whether...

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.

Solutions

Expert Solution

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%


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