Question

The time it takes people to read a certain book is normally distributed with a mean of 147 minutes and a standard deviation of 12 minutes.
Approximately what percent of people take between 123 and 171 minutes to read the book?

Answer 1

Answer: 95.7%

Step-by-step explanation:

Since the time it takes people to read the book is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = the time it takes people to read the book.

µ = mean time

σ = standard deviation

From the information given,

µ = 147 minutes

σ = 12 minutes

The probability that a person takes between 123 and 171 minutes to read the book is expressed as

P(123 ≤ x ≤ 171)

For x = 123,

z = (123 - 147)/12 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

For x = 171,

z = (171 - 147)/12 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.98

Therefore,

P(123 ≤ x ≤ 171) = 0.98 - 0.023 = 0.957

The percentage of people that take between 123 and 171 minutes to read the book is

0.957 × 100 = 95.7%