Question

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 3 minutes. Sixty percent of the time, it takes more than how many minutes to find a parking space? (Round your answer to two decimal places.)

Answer 1

Here The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 3 minutes.

so if x is the time taken by a person to find a parking space, then

x ~ NORMAL (5 mins, 3 mins)

so as asked if x is the time above which it takes to find the parking space 60 % of the time, then writing it mathematically.

P(x > x₀)= 0.6

P(x < x₀) = 0.4

so now finding z value

z = NORMSINV(0.4) = -0.25335

so here

z =(x₀ - 5)/3

x₀ = 5 - 3 * 0.2535

x₀ = 4.24 mins