Question

The mean number of words per minute (WPM) read by sixth graders is 83 with a standard deviation of 12 WPM. If 89 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 1.4 WPM? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 83

standard deviation = = 12

n = 89

= = 83

= / n = 12 / 89 = 1.2720

P( 81.6 < < 84.4) = 1 - (P((81.6 - 83) / 1.2720 <( - ) / < (84.4 - 83) / 1.2720)))

= 1 - P(-1.10 < Z < 1.10)

= 1 - (P(Z < 1.10) - P(Z < -1.10) ) Using standard normal table,  

= 1 - ( 0.8643 - 0.1357 )

= 1 - 0.7286

Probability = 0.2714