Question

scores on a test are normally distributed with a mean of 81 and a standard deviation of 8. Find the probability that a randomly chosen score will be between 70 and 93.

Answer 1

0.8486

Step-by-step explanation:

To find the probability that a score will be between 70 and 93, we first need to standardize these values, so we will use the following

`z=\frac{value-mean}{standard\text{ deviation}}`

Therefore, for 70 and 93, we get

`\begin{gathered} z=(70-81)/(8)=-1.375 \\ \\ z=(93-81)/(8)=1.5 \end{gathered}`

Then, we need to find the following probability

P(-1.375 < z < 1.5)

This probability can be calculate using a standard normal table, so

P(-1.375 < z < 1.5) = P(z < 1.5) - P(z < -1.375)

P(-1.375 < z < 1.5) = 0.9332 - 0.0846

P(-1.375 < z < 1.5) = 0.8486

Therefore, the probability is 0.8486