In: Statistics and Probability
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.
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%