Question

A journal published a study of the lifestyles of visually impaired students. Using​ diaries, the students kept track of several​ variables, including number of hours of sleep obtained in a typical day. These visually impaired students had a mean of 9.06hours and a standard deviation of 2.11 hours. Assume that the distribution of the number of hours of sleep for this group of students is approximately normal. Complete parts a through c.

A. Find P(x<6)

b. Find P(8≤x≤10)

c. Find the value a for which P(x<a)= 0.3

Answer 1

Solution :

(a)

P(x < 6) = P[(x - ) / < (6 - 9.06) / 2.11]

= P(z < -1.45)

= 0.0735

(b)

P(8 x 10) = P[(8 - 9.06)/ 2.11) (x - ) /   (10 - 9.06) / 2.11) ]

= P(-0.50 z 0.45)

= P(z 0.45) - P(z -0.50)

= 0.3651

(c)

P(Z < -0.524) = 0.3

z = -0.524

Using z-score formula,

x = z * +

x = -0.524 * 2.11 + 9.06 = 7.95

a = 7.95