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 more than five hours to construct a soapbox derby car.
A) 0
B) 0.0228
C) 0.4772
D) 0.9772

Question

Quizplus · Accepted Answer

To find the probability that it takes more than five hours to construct a soapbox derby car, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (5 hours), μ is the mean (3 hours), and σ is the standard deviation (1 hour). Plugging in the values, we get Z = (5 - 3) / 1 = 2. Looking up a Z-score of 2 in the standard normal distribution table or using a calculator, we find the area to the left of Z=2 is approximately 0.9772. Since we're interested in the probability of taking more than 5 hours, we subtract this from 1 to get 1 - 0.9772 = 0.0228.

The Time to Complete the Construction of a Soapbox Derby