If a study shows that the amount of time a student sleeps on any given nights...

If a study shows that the amount of time a student sleeps on any given nights is normally distributed with a mean of 7.2 hours and a standard deviation of 3 hours.

Find the probability of one randomly selected student sleeping less than 8 hours.

Expert Solution

X: amount of time a student sleeps on any given nights

X follows normal distribution with mean of 7.2 hours and a standard deviation of 3 hours

probability of one randomly selected student sleeping less than 8 hours = P(X<8)

Z-score for 8 = (8-mean) / standard deviation = (8-7.2)/3 = 0.8/3 = 0.27

From standard normal tables ,

P(Z<0.27) = 0.6064

P(X<8) = P(Z<0.27) = 0.6064

Probability of one randomly selected student sleeping less than 8 hours = P(X<8) = 0.6064

Probability of one randomly selected student sleeping less than 8 hours = 0.6064

orchestra answered 2 years ago

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