use technology or a z - score table to answer the question. the scores on a memory test are normally…

use technology or a z - score table to answer the question. the scores on a memory test are normally distributed with a mean of 100 and a standard deviation of 25. consider a group of 400 people who take the test. how many people will score 90 or less? 63 138 180 262

use technology or a z - score table to answer the question. the scores on a memory test are normally distributed with a mean of 100 and a standard deviation of 25. consider a group of 400 people who take the test. how many people will score 90 or less? 63 138 180 262

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 90$, $\mu=100$, and $\sigma = 25$. So $z=\frac{90 - 100}{25}=\frac{- 10}{25}=-0.4$.

Step2: Find the cumulative probability

Using a z - score table, the cumulative probability $P(Z\leq - 0.4)$ is approximately $0.3446$.

Step3: Calculate the number of people

Multiply the cumulative probability by the total number of people. So the number of people who score 90 or less is $0.3446\times400 = 137.84\approx138$.

Answer:

138