Question

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the sample mean will be less than or equal to 186 is

Answer 1

A population has a mean = 180

And standard deviations , = 24

A sample of n=64 taken from population.

Then mean of is =180

And standard deviations of is = /√n = 24/√64 =24/8 = 3

We have to find the probability that sample mean is less than 186.

ie, P( 186)

= P( - )/ 186 -180/3)

=P( z 2)

= 0.9772 ( from standard normal table)

So,the probability that sample mean will be less than or equal to 186 is 0.9772.