Question

Show all work in the space provided. All work must be shown to obtain full credit. If a calculator function was used, list exactly what was entered into the calculator. All z-score calculations must be shown.

1. According to one study, the average hours of sleep on a weeknight for men was 6.9 hours with a standard deviation of 1.5 hours.

a. Find the proportion of men who sleep for more than 8 hours per night.

b. Find the proportion of men who sleep for less than 6 hours per night.

c. Find the proportion of men who sleep between 6-8 hours per night.

d. Find the number of hours that represents the 90th percentile.

Answer 1

1.

Suppose, random variable X denotes duration of sleep (in hours).

(a)

Required probability is given by

  [Using calculator code 'normalcdf(0.7333333, 5, 0, 1)']

Note- We know that 99.73% of values lie within 3 standard deviation. So, in place of upper limit we considered 5.

(b)

Required probability is given by

   [Using calculator code 'normalcdf(-5, -0.6, 0, 1)']

(c)

Required probability is given by

   [Using calculator code 'normalcdf(-0.6, 0.7333333, 0, 1)']

(d)

We have to calculate c so that,

    [Using calculator code 'invNorm(0.90, 0, 1)']

Hence, 8.822328 hours represents the 90 th percentile.