Question

The Journal of Visual Impairment & Blindness (May-June 1997) published a study of the lifestyles of visually impaired students. Using diaries, the students kept track of several variables, including the number of hours of sleep obtained in a typical day. These visually impaired students had a mean of 9.06 hours 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. a. Find the probability that a visually impaired student obtains more than 10 hours of sleep on a typical day. (5 points) b. Find the probability that a visually impaired student gets between 7 and 8 hours of sleep on a typical night. (5 points)

Answer 1

Solution :

Given that ,

mean = = 9.06 hours

standard deviation = = 2.11 hours

a) P(x > 10) = 1 - p( x< 10)

=1- p P[(x - ) / < (10 - 9.06) / 2.11]

=1- P(z < 0.45)

Using z table,

= 1 - 0.6736

= 0.3264

b) P( 7 < x < 8) = P[(7 - 9.06 ) / 2.11) < (x - ) /  < (8 - 9.06) / 2.11 ) ]

= P( -0.98 < z < -0.50)

= P(z < -0.50) - P(z < -0.98)

Using z table,

= 0.3085 - 0.1635

= 0.1450