Question

A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is

Answer 1

Solution :

Given that,

mean = = 180

standard deviation = = 36

n = 84

= = 180

= / n = 36 / 84 = 3.93

P(181 < < 185 )  

= P[(181 - 180) / 3.93 < ( - ) / < (185 - 180) / 3.93)]

= P( 0.25 < Z < 1.27 )

= P(Z < 1.27 ) - P(Z < 0.25)

Using z table,  

= 0.8980 - 0.5987

= 0.2993