Question

Completion times for a reading test are normally distributed with
a mean time of 73,4 minutes and a standard deviation of 7.4
minutes.
Approximately what percent of the completion times is
between 73.4 and 88.2 minutes?
a.
b.
Ans 2a
Approximately what percent of the completion times is at
most 58.6 minutes?
Ans 2b

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