on a test that has a normal distribution, a score of 63 falls three standard deviations above the mean, and…
on a test that has a normal distribution, a score of 63 falls three standard deviations above the mean, and a score of 15 falls three standard deviations below the mean. determine the mean of this test.
Answer
Answer:
39
Explanation:
Step1: Let mean be $\mu$ and standard - deviation be $\sigma$.
We have the equations: $\mu + 3\sigma=63$ and $\mu - 3\sigma = 15$.
Step2: Add the two equations.
$(\mu + 3\sigma)+(\mu - 3\sigma)=63 + 15$.
Step3: Simplify the left - hand side.
$2\mu=78$.
Step4: Solve for $\mu$.
$\mu=\frac{78}{2}=39$.