The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car.
A) 0.3085
B) 0.3830
C) 0.6170
D) 0.6915

Question

Quizplus · Accepted Answer

Using the z-score formula, we get:

z1 = (2.5 - 3) / 1 = -0.5
z2 = (3.5 - 3) / 1 = 0.5

Then, using a standard normal distribution table, we find the area between z1 and z2:

P(-0.5 < Z < 0.5) = 0.3830

Therefore, the probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car is 0.3830, which corresponds to choice B).

The Time to Complete the Construction of a Soapbox Derby