# 非常緊急兩小時內要交...需要數學專家幫忙(要會英文)

Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.78 hours of sleep, with a standard deviation of 2.49 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

(1)What is the probability that a visually impaired student gets less than 6.5 hours of sleep?

(2) What is the probability that a visually impaired student gets between 6.4 and 7.54 hours of sleep?

(3) Fourty percent of students get less than how many hours of sleep on a typical day?

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Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.78 hours of sleep, with a standard deviation of 2.49 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

(1)What is the probability that a visually impaired student gets less than 6.5 hours of sleep?

P(X<6.5) = P(Z<(6.5-9.78)/2.49) = 9.39%

(2) What is the probability that a visually impaired student gets between 6.4 and 7.54 hours of sleep?

P(6.4<X<7.54) = P((6.4-9.78)/2.49<Z<(7.54-9.78)/2.49) = 18.4167% - 8.7322% = 9.6845%

(3) Fourty percent of students get less than how many hours of sleep on a typical day?

P(Z<-0.25335) = 40% ==> (X-9.78)/2.49 = -0.25335 ==> X = 9.149165 hours