Question

The mean number of words per minute (WPM) typed by a speed typist is 149 with a standard deviation of 14 WPM. What is the probability that the sample mean would differ from the population mean by less than 2.3 WPM if 88 speed typists are randomly selected? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 149

standard deviation = = 14

n = 88

=   = 149

= / n = 14 / 88 = 1.4924

P(146.7 < < 151.3) = P((146.7 - 149) / 1.4924 <( - ) / < (151.3 - 149) / 1.4924))

= P(-1.54 < Z < 1.54)

= P(Z < 1.54) - P(Z < -1.54) Using standard normal table,  

= 0.9382 - 0.0618

= 0.8764

Probability = 0.8764