Question

Previous Page Next Page Page 10 of 10 Question 10 (4 points) A company in California is concerned about the time that its employees spend commuting to work. The one-way commute times for its employees are normally distributed with a mean of 35.5 minutes and a standard deviation of 5.0 minutes. What is the commute time that separates the longest 20.9% of commutes from the rest? [ENTER ANSWER AS A NUMBER OF MINUTES TO 2 DECIMAL PLACES, e.g. 15min 40sec would be entered as "15.67"] Your Answer: Answer Previous Page Next Page Page 10 of 10 Submit Quiz

Answer 1

Q.10) Given that, mean $(\mu)$ = 35.5 minutes and

standard deviation $(\sigma)$ = 5.0 minutes

We want to find, the value of x such that, P(X > x) = 20.9%

$=> P(\frac { X-\mu}{\sigma} <\frac{ x-35.5}{5.0}) = 0.791$

$=> P(Z<\frac{ x-35.5}{5.0}) = 0.791$

$=> \frac{ x-35.5}{5.0} = Z_{0.791}$

$=> \frac{ x-35.5}{5.0} = 0.81$

Answer: 39.55 minutes