the amount of sleep that elementary school children get per night follows a normal distribution with a mean of 9.5 hours and a standard deviation of 0.55 hours. is it unusual for an elementary student to get at least 12 hours of sleep?

If the mean is 9.5 and the standard deviation is 0.55, then anything within the normal curve of 10.05 on the high end and 8.45 on the low end is normal. 12 is more than several standard deviations or an outlier if this makes sense.

So, it is unusual as the problem is stated, but if it's a weekend, 12 hours is normal. LOL

Good luck!

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fichoh fichoh · Answer 2 · 2021-10-19T13:24:28+02:00

Based on the normal distribution parameters given, the probability of a student getting atleast 12 hours of sleep ls 0. Hence, it is abnormal.

Given the Parameters :

Mean = 9.5
Standard deviation = 0.55

Using the Zscore formula, the probability of getting a atleast 12 hours of sleep can be expressed thus :

Zscore = (Score - Mean) / standard deviation

For X ≥ 12 :

Z = (12 - 9.5) / 0.55 = 4.545

The probability using a normal distribution table :

P(Z ≥ 4.54) = 1 - P(Z ≤ 4.54)

P(Z ≤ 4.54) = 1 ( normal distribution table)

P(Z ≥ 4.54) = 1 - 1 = 0

Since, the probability is 0 ; hence, it is unlikely and therefore, abnormal.

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