Question

the scores on a test are normally distributed with a mean of 90 and a standard deviation of 18. what is the score that is 2\frac{1}{2} standard deviations above the mean? a score of is 2\frac{1}{2} standard deviations above the mean.

Explanation:

Step1: Identify given values

Mean $\mu = 90$, standard - deviation $\sigma=18$, number of standard deviations $z = 2.5$.

Step2: Use the formula for a value in a normal distribution

The formula is $x=\mu + z\sigma$. Substitute the values: $x = 90+2.5\times18$.

Step3: Calculate the result

First, calculate $2.5\times18 = 45$. Then, $x=90 + 45=135$.

Answer:

135