In a survey of 215 adult Americans, it was found that the average amount of sleep per night is 7.8 hours with a standard deviation of 1.2 hours. How many adult Americans would need to be surveyed to estimate the mean amount of sleep per night within 0.12 hour with 95% confidence?

We would need at least 385 adult Americans.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

How many adult Americans would need to be surveyed to estimate the mean amount of sleep per night within 0.12 hour with 95% confidence?

You would need at least n adults, in which n is found when M = 0.12, . So

Rounding up, 385

We would need at least 385 adult Americans.

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step-by-step explanation:

i used the pitagoras theoreme