Suppose that the amount of time it takes to develop a new iPhone app is normally distributed with an average of 8 weeks and a standard deviation of 2 weeks.Fill in the blank in the following sentence: "There is a 25% probability that development time will be between how many weeks and 8 weeks."
A)2.0
B)6.0
C)6.7
D)7.8
E)8.6

Question

Quizplus · Accepted Answer

Given that the distribution is normal and we are looking for the time frame that represents the middle 25% leading up to the mean (8 weeks), we need to find the z-score that corresponds to the lower 37.5% percentile (since 50% - 25% = 25%, and we're looking for the value that leaves 37.5% below it to get to the middle 50%). The z-score for the 37.5th percentile is approximately -0.32. Using the z-score formula $Z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value we're looking for, $\mu = 8$ weeks is the mean, and $\sigma = 2$ weeks is the standard deviation, we can solve for $X$. Plugging in the values, $-0.32 = \frac{(X - 8)}{2}$, solving for $X$ gives us approximately 6.7 weeks.

Suppose That the Amount of Time It Takes to Develop