Question

Hugo averages 72 words per minute on a typing test with a standard deviation of 7 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(72,7).

Suppose Hugo types 80 words per minute in a typing test on Wednesday. The z-score when x=80 is ________. This z-score tells you that x=80 is ________ standard deviations to the ________ (right/left) of the mean, ________.

Correctly fill in the blanks in the statement above.

Select the correct answer below:

Suppose Hugo types 80 words per minute in a typing test on Wednesday. The z-score when x=80 is −0.8. This z-score tells you that x=80 is 0.8 standard deviations to the left of the mean, 72.

Suppose Hugo types 80 words per minute in a typing test on Wednesday. The z-score when x=80 is 0.8. This z-score tells you that x=80 is 0.8 standard deviations to the right of the mean, 72.

Suppose Hugo types 80 words per minute in a typing test on Wednesday. The z-score when x=80 is 1.143. This z-score tells you that x=80 is 1.143 standard deviations to the right of the mean, 72.

Suppose Hugo types 80 words per minute in a typing test on Wednesday. The z-score when x=80 is −1.143. This z-score tells you that x=80 is 1.143 standard deviations to the left of the mean, 72.

Answer 1

Solution :

Given that ,

mean = = 72

standard deviation =  = 7

x = 80

Using z-score formula,

z = x - /   

z = 80 - 72 / 7

z = 1.143

Suppose Hugo types 80 words per minute in a typing test on Wednesday. The z-score when x=80 is 1.143. This z-score tells you that x=80 is 1.143 standard deviations to the right of the mean, 72.