Question

The Mean number of words per minute (WPM) read by sixth graders is 98 with a standard deviation of 20. If 57 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 4.41 WPM? ( round your answer to 4 Decimal places and show work)

Answer 1

Solution :

Given that,

mean = = 98

standard deviation = = 20

n = 57

= 98

= / n = 20 / 57 = 2.649

= 1 - P(98 - 4.41 < < 98 + 4.41)

= 1 - P(93.59 < < 102.41)

= 1 - P((93.59 - 98) / 2.649 <( - ) / < (102.41 - 98) / 2.649))

= 1 - P(-1.6648 < Z < 1.6648)

= 1 - {P(Z < 1.6648) - P(Z < -1.6648)}

= 1 - {0.952 - 0.048}

= 1 - 0.904

= 0.096

Probability = 0.0960