Answer:
9.34 hours
Step-by-step explanation:
Mean number of hours (μ) = 7.8 hours
Standard deviation (σ) = 1.2 hours
According to a z-score table, the corresponding z-score to the 90th percentile of a normal distribution is z = 1.281
For any number of hours adult women sleep in a day, X, the z-score is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
If z = 1.281, the value of X is:
[tex]1.281=\frac{X-7.8}{1.2}\\X=9.34\ hours[/tex]
The number of hours that represents the 90th percentile is 9.34 hours.
Answer: 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
