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dimulka [17.4K]
3 years ago
6

The distribution of the average amount of sleep per night gotten by college students is roughly bell-shaped with mean 412 minute

s and standard deviation 68 minutes. The proportion of those who get an average of less than eight hours (480 minutes) of sleep per night is about:
Mathematics
1 answer:
kirza4 [7]3 years ago
4 0

Answer:

P(X

P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(412,68)  

Where \mu=412 and \sigma=68

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard table or excel and we got:

P(z

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