Question

The heights of adult men in a certain country are normally distributed with a mean of 70.4 inches and a standard deviation of 2.5 inches.

a. What are the standard score and percentile of a height of 73 ​inches?

The standard score is z = __________ ​(Round to two decimal places as​ needed.)

The percentile is the ______ percentile. ​(Round to two decimal places as​ needed.)

b. What are the standard score and percentile of a height of 69 ​inches?

The standard score is z = ____________ ​(Round to two decimal places as​ needed.)

The percentile is the ________________ percentile. ​(Round to two decimal places as​ needed.)

c. What percentage of the adult male population of this country is taller than 6 prime 2 double prime​?

The percentage taller than 6 prime 2 double prime is ________​%.

For the following​ event, state whether you think the difference between what occurred and what you would expect by chance is statistically significant. Explain.

Eleven winners of the Power Ball lottery in a row bought their tickets at the same​ 7-Eleven store. ?

A.It is significant because, one winner is​ unlikely, two winners is very​ unlikely, and 11 winners is certainly below a 0.01 probability level.

B. It is not significant because, in 11 lotteries there are 11 winners.

C. It is not significant because, the difference between the expected number​ winners, 11​, and the actual number of​ winners, 11​, is zero.

D. It is significant because, one winner is​ unlikely, two winners is very​ unlikely, and 11 winners is certainly above a 0.05 probability level.

Answer 1

a) standard score is z = (X-mean)/std deviation =(73-70.4)/2.5 =1.04

The percentile is the 85.08 percentile

b)

standard score is z = -0.56

The percentile is the 28.77 percentile

(here if it is 6 ft 2inch or 74 inch)

percentage of the adult male population of this country is taller than 6 prime 2 double prime​ =7.49%

A.It is significant because, one winner is​ unlikely, two winners is very​ unlikely, and 11 winners is certainly below a 0.01 probability level.