Suppose the total number of hours adult women sleep in a day are normally distributed with a mean of 7.8 hours and a standard deviation of 1.2 hours. What number of hours represents the 90th percentile?

9.342 hours represents the 90th percentile

Step-by-step explanation:

Since the total number of hours that adult women sleep in a day are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = number of hours.

µ = mean

σ = standard deviation

From the information given,

µ = 7.8 hours

σ = 1.2 hours

The 90th percentile is 90/100 = 0.9

Looking at the normal distribution table, the corresponding z score is 1.285

For z = 1.285,

1.285 = (x - 7.8)/1.2

Cross multiplying by 1.2, it becomes

1.2 × 1.285 = x - 7.8

1.542 = x - 7.8

x = 1.542 + 7.8

x = 9.342

if x = 1, then the answer is 3.5

i got 10.28 but that rounds up to 10.3