according to a recent study, the mean number of hours college students spent playing video games per month was 43 hours with a population standard deviation of 2 hours. two weeks before final exams were scheduled to begin, 100 college students were randomly selected. what is the probability that the mean number of hours spent playing video games is less than 42.8 hours? use the z-table below. round your answer to three decimal places if necessary.

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14-11-2022
Mathematics

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according to a recent study, the mean number of hours college students spent playing video games per month was 43 hours with a population standard deviation of 2 hours. two weeks before final exams were scheduled to begin, 100 college students were randomly selected. what is the probability that the mean number of hours spent playing video games is less than 42.8 hours? use the z-table below. round your answer to three decimal places if necessary.

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qwterabite qwterabite · Answer 1 · 2022-11-27T03:47:20-05:00

The probability that the mean number of hours spent playing video games is less than 42.8 hours is 0.15866

we are given the mean of ( m )= 43 hours and the standard deviations (s) of 2 hours, where the sample size (n) = 100.

Obtain the Zscore ;

Z = (x - m) ÷s/sqrt(n)

Z = (42.8 - 43) ÷ 2/sqrt(100)

Z = - 0. 2 ÷ 0.2

Z = - 1

so we need the probability of P(Z < - 1), from the table of z-score the probability of a z-score of -1 is 0.15866.Hence, the probability that the mean number of hours spent playing video games is less than 42.8 hours is 0.15866

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