Question

The results of a national survey showed that on average, adults sleep 7 hours per night. Suppose that the standard deviation is 1.5 hours and that the number of hours of sleep follows a bell-shaped distribution. If needed, round your answers to two decimal digits. If your answer is negative use “minus sign”.

(a)	Use the empirical rule to calculate the percentage of individuals who sleep between 4 and 10 hours per day.
	Enter your answer as a percentage.
	%
(b)	What is the z-value for an adult who sleeps 8 hours per night?
(c)	What is the z-value for an adult who sleeps 6 hours per night?

Answer 1

Mean = 7 hours

Standard deviation = 1.5 hours

a) According to the empirical rule, 68%, 95% and 99.7% of data values lie within 1, 2 and 3 standard deviations of mean.

7-2x1.5 = 4

7+2x1.5 = 10

4 and 10 are values that are 2 standard deviations from mean.

Therefore, percentage of individuals who sleep between 4 and 10 hours = 95%

b) Z = (x - mean)/standard deviation

When x = 8,

Corresponding z score is (8-7)/1.5

= 0.67

c) When x = 6,

Corresponding z score is (6-7)/1.5

= -0.67