Question

1. the daily commute times for employees at a large law firm are normally distributed, with mean of 54 minutes and a standard deviation of 9 minutes. bobby’s commute time is 54 minutes, lindsay’s commute time, when converted to a z - score, is -0.1, and helen’s commute time is longer than 40% of employees at the law firm. who has the shortest commute time? a. bobby b. lindsay c. helen d. bobby, lindsay, and helen all have the same commute times. e. this question cannot be answered without more information.

Explanation:

Step1: Analyze Bobby's commute time

Bobby's commute time is equal to the mean ($\mu = 54$ minutes), so his z - score is $z_{Bobby}=\frac{54 - 54}{9}=0$.

Step2: Analyze Lindsay's z - score

Lindsay's z - score is given as $z_{Lindsay}=- 0.1$.

Step3: Analyze Helen's commute time

If Helen's commute time is longer than 40% of employees, we look up the z - score in the standard normal distribution table. The z - score corresponding to a cumulative probability of 0.4 is approximately $z_{Helen}\approx - 0.25$.

Step4: Compare z - scores

Since $-0.25<-0.1 < 0$, Helen has the lowest z - score. A lower z - score indicates a shorter commute time in a normal distribution.

Answer:

C. Helen