Question

The mean number of words per minute (WPM) typed by a speed typist is 72 with a variance of 100. What is the probability that the sample mean would differ from the population mean by more than 3.3 WPM if 43 speed typists are randomly selected? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 72

² = 100

standard deviation = = 10

n = 43

= 72

= / n = 10 / 3.3 = 5.50482

1 - P(68.7 < < 75.3)

= 1 - P((68.7 - 72) / 5.50482 <( - ) / < (75.3 - 72) / 5.50482))

= 1 - P(-0.60 < Z < 0.60)

= 1 - P(Z < 0.60) - P(Z < -0.60) Using z table,

= 1 - [0.7257 - 0.2743]

= 1 - 0.4514

Probability = 0.5486