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Elden [556K]
3 years ago
5

College students average 8.6 hours of sleep per night with a standard deviation of 35 minutes. If the amount of sleep is normall

y distributed, what proportion of college students sleep for more than 9.6 hours? _
Mathematics
1 answer:
Soloha48 [4]3 years ago
7 0

Answer:

4.27%

Step-by-step explanation:

We have been given that college students average 8.6 hours of sleep per night with a standard deviation of 35 minutes. We are asked to find the probability of college students that sleep for more than 9.6 hours.

We will use z-score formula to solve our given problem.

z=\frac{x-\mu}{\sigma}

z = z-score,

x = Random sample score,

\mu = Mean,

\sigma = Standard deviation.

Before substituting our given values in z-score formula, we need to convert 35 minutes to hours.

35\text{ min}=0.58\text{ Hour}

z=\frac{9.6-8.6}{0.58}

z=\frac{1}{0.58}

z=1.72

Now, we need to find P(z>1.72).

Using formula P(z>a)=1-P(z, we will get:

P(z>1.72)=1-P(z

Using normal distribution table, we will get:

P(z>1.72)=1-0.95728

P(z>1.72)=0.04272

0.04272\times 100\%=4.272\%

Therefore, 4.27% of college students sleep for more than 9.6 hours.

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