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%
