Question

the scores on a test are normally distributed with a mean of 200 and a standard deviation of 30. find the score that is 3 1/2 standard deviations above the mean. a score of is 3 1/2 standard deviations above the mean.

Explanation:

Step1: Identify the formula

The formula for a value $x$ in a normal - distribution is $x=\mu + z\sigma$, where $\mu$ is the mean, $z$ is the number of standard - deviations from the mean, and $\sigma$ is the standard deviation.

Step2: Substitute the given values

We are given that $\mu = 200$, $z = 3.5$, and $\sigma=30$.
Substitute into the formula: $x=200 + 3.5\times30$.

Step3: Perform the calculation

First, calculate $3.5\times30 = 105$.
Then, $x=200 + 105=305$.

Answer:

305