Dallas Green Homes uses a normal curve to estimate next year's demand.The distribution has a mean of 163 units and a standard deviation of 36 units.According to this demand distribution, there's a 5% chance that demand will be no more than how many units.
A)87.2
B)123.4
C)75.6
D)103.6
E)102.1

Question

Quizplus · Accepted Answer

To find the demand level that has a 5% chance of occurring, we look for the z-score corresponding to the bottom 5% of a normal distribution, which is approximately -1.645. Using the z-score formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the demand level, $\mu = 163$ units is the mean, and $\sigma = 36$ units is the standard deviation, we solve for $X$. Rearranging the formula gives $X = \mu + z\sigma = 163 + (-1.645)(36) \approx 103.6$ units.

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