QuestionThe scores on a test are normally distributed with a mean of 200 and a standard deviation of 10 . Find the score that is $1 \frac{1}{2}$ standard deviations above the mean.
A score of $\square$ is $1 \frac{1}{2}$ standard deviations above the mean.

Studdy Solution
Calculate the score that is $1.5$ standard deviations above the mean using the formula:
$$\text{Score} = \mu + (z \times \sigma)$$
where $z = 1.5$, $\mu = 200$, and $\sigma = 10$.
$$\text{Score} = 200 + (1.5 \times 10)$$
$$\text{Score} = 200 + 15$$
$$\text{Score} = 215$$
A score of $\boxed{215}$ is $1 \frac{1}{2}$ standard deviations above the mean.