Question

The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.1 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 4.7 and 9.1 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

Solution :

Given that ,

mean = =6.9

standard deviation = = 1.1

(A)P(4.7< x < 9.1) = P[(4.7 - 6.9) /1.1 < (x - ) / < (9.1- 6.9 ) /1.1 )]

= P(-2< Z < 2)

= P(Z <2)+P(Z <-2 )

using empirical rule

=95%/2 + 95%/2

=47.52%+47.52%

=95%

(B)using z - score formula

= (x - ) /

=(8 -6.9)/1.1

=1

z=1

(C)

using z - score formula

= (x - ) /

=(6 -6.9)/1.1

= - 0.82

z= - 0.82