JewelMist.com estimates the cost of relocating its headquarters to Los Gatos, CA with a normal distribution centered on $9.5 million and having a standard deviation of $1.1 million.According to this distribution, there's a 60% chance that costs will be less than how many millions of dollars.
A)9.367
B)9.162
C)8.756
D)10.428
E)9.775

Question

Quizplus · Accepted Answer

To find the value associated with a 60% chance of being less than a certain cost, we look for the z-score corresponding to 60% in a standard normal distribution table. The z-score for 60% (or 0.60 probability) is approximately 0.25. Using the z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value we're solving for, $\mu$ is the mean, and $\sigma$ is the standard deviation, we rearrange to solve for $X$: $X = Z\sigma + \mu$. Substituting the given values ($\mu = 9.5$ million, $\sigma = 1.1$ million, and $Z = 0.25$), we get $X = 0.25(1.1) + 9.5 = 0.275 + 9.5 = 9.775$ million dollars.

JewelMistCom Estimates the Cost of Relocating Its Headquarters to Los