Question

# Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted....

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 8.9 hours of sleep, with a standard deviation of 2.37 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

(a)  What is the probability that a visually impaired student gets less than 6.6 hours of sleep?

(b)  What is the probability that a visually impaired student gets between 6.3 and 10.65 hours of sleep?

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

Solution :

(a)

P(x < 6.6) = P[(x - ) / < (6.6 - 8.9) / 2.37]

= P(z < -0.97)

= 0.1660

(b)

P(6.3 < x < 10.65) = P[(6.3 - 8.9)/ 2.37) < (x - ) /  < (10.65 - 8.9) / 2.37) ]

= P(-1.10 < z < 0.74)

= P(z < 0.74) - P(z < -1.10)

= 0.6347

(c)

P(Z < -0.524) = 0.30

z = -0.524

Using z-score formula,

x = z * +

x = -0.524 * 2.37 + 8.9 = 7.66

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