Here is a list of number of speeding tickets written by 5 state troopers in Feb

Question

Here is a list of number of speeding tickets written by 5 state troopers in Feb 2017. The mean of this distribution is 70 and the standard deviation is 5. Number of Speeding Tickets 90 70 75 60 50 80

a. Take each score from the distribution shown above, and transform it into a z score

b. Take the z score for 50 speeding tickets, and find the proportion of cases between the mean and that z score Is this value low or high?

c. Take the z score for 90 speeding tickets, and find the proportion of cases that is less than that z score Is this value low or high?

d. Take the z score for 80 speeding tickets, and find the proportion of cases that is greater than this z score . Is this value low or high?

Explanation / Answer

Z score = (number - mean)/standard deviation

A) For the number 90, z score = (90 - 70)/5 = 4

For the number 70, z score = (70 - 70)/5 = 0

For the number 75, z score = (75 - 70)/5 = 1

For the number 60, z score = (60 - 70)/5 = -2

For the number 50, z score = (50 -70)/5 = -4

B) Proportion fo scores between mean and z score value = P(z = 0) - P(z = -4)

= 0.5 - 0.000032

= 0.499968

This value is low

C) P(z < 4) = 0.999968

This value is high

D) P(z > 2) = 1 - P(z < 2)

= 1 - 0.97725

= 0.02275

This value is low

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