Question

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]

Answer 1

Solution:-

Given that,

mean = = 35.5

standard deviation = = 5.0

Using standard normal table,

P(Z > z) = 20.9%

= 1 - P(Z < z) = 0.209  

= P(Z < z) = 1 - 0.209

= P(Z < z ) = 0.791

= P(Z <0.8099 ) = 0.791

z =0.8099

Using z-score formula,

x = z * +

x = 0.8099 *5.0+35.5

x = 39.5495

x =39.55