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 within 3 of the population mean is:

Answer 1

Solution :

Given that,

mean = = 180

standard deviation = = 24

n = 64

= = 180

= / n = 24/ 64 = 3

P(177 < < 183) = P((177 - 180) / 3<( - ) / < (183 - 180) / 3))

= P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1) Using standard normal table,  

= 0.8413 - 0.1587

= 0.6826

Probability = 0.6826