11: For 2016, the Census Bureau identified the average commute time for an Arkan

Question

11: For 2016, the Census Bureau identified the average commute time for an Arkansas was 24.8 minutes with a standard deviation of 6 minutes. Answer the following questions: (Show your z score formula/calculations. Round z scores to two decimal places (i.e., 1.96) and probability to four decimal places (i.e., .7777)).

A) What is the probability of a random Arkansan commuter taking less than 18 minutes?

B) What is the probability of a random Arkansas commuter taking more than 30 minutes?

C) What is the probability of a random Arkansan commuter taking between 18 and 30 minutes?

Explanation / Answer

mean = 24.8 , s = 6

a)

P(X < 18)

z = ( x - mean)/ s
= ( 18 - 24.8)/ 6
= -1.133

P(X < 18) = P(Z < -1.133) = 0.1285

b)

P(X > 30)

z = ( x - mean)/ s
= ( 30 - 24.8)/ 6
= 0.8667

P(X > 30) = P(Z > 0.8667) = 0.1931

c)

P(18 < X < 30)

z = ( x - mean)/ s
= ( 18 - 24.8)/ 6
= -1.133

z = ( x - mean)/ s
= ( 30 - 24.8)/ 6
= 0.8667

P(18 < X < 30) = P(-1.133 < Z < 0.8667) = 0.6784
  

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