Question

Completion times for a reading test are normally distributed with

Answer 1

Answer:

47.72%  of the completion times is  between 73.4 and 88.2 minutes

2.28% of the completion times is at  most 58.6 minutes

Step-by-step explanation:

A reading test are normally distributed with  a mean time of 73,4 minutes and a standard deviation of 7.4  minutes.

$\mu = 73.4 minutes$

Standard deviation = $\sigma = 7.4 minutes$

A)Approximately what percent of the completion times is  between 73.4 and 88.2 minutes i.e.P(73.4<x<88.2)

Formula : $Z=\frac{x-\mu}{\sigma}$

At x = 73.4

$Z=\frac{73.4-73.4}{7.4}$

Z=0

Refer the z table for p value

p value = 0.5

At z = 88.2

$Z=\frac{88.2-73.4}{7.4}$

Z=2

Refer the z table for p value

p value =0.9772

So,P(73.4<x<88.2)=0.9772-0.5=0.4772

So, 47.72%  of the completion times is  between 73.4 and 88.2 minutes

B)Approximately what percent of the completion times is at  most 58.6 minutes i.e. $P(X\leq 58.6)$?

$Z=\frac{x-\mu}{\sigma}$

$Z=\frac{58.6-73.4}{7.4}$

Z=-2

Refer the z table for p value

p value =0.0228

So,2.28% of the completion times is at  most 58.6 minutes