Monday

March 2, 2015

March 2, 2015

Posted by **Mia** on Friday, May 9, 2014 at 8:41pm.

a. What is the probability that a randomly selected person sleeps more than 8 hours (to 4 decimals)?

b. What is the probability that a randomly selected person sleeps 6 hours or less (to 4 decimals)?

c. Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep (to the nearest whole number)?

- Economics (37) -
**Kuai**, Friday, May 9, 2014 at 9:00pm37) According to the Sleep Foundation, the average night's sleep is 6.8 hours (Fortune, March 20, 2006). Assume the standard deviation is .7 hours and that the probability distribution is normal.

a. What is the probability that a randomly selected person sleeps more than 8 hours (to 4 decimals)?

P( x > 8)

z = ( x - μ ) / σ

z = ( 8 - 6.8 ) / .7

z = 1.714

P(z > 1.714) = 1-0.9564 = 0.0436

b. What is the probability that a randomly selected person sleeps 6 hours or less (to 4 decimals)?

P ( x < 6)

z = ( x - μ ) / σ

z = ( 6 - 6.8 ) / .7

z = -1.14

P( z <-1.14) = 0.1271

c. Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep (to the nearest whole number)?

P( 7 < x < 9)

z = ( x - μ ) / σ

z = ( 7 - 6.8 ) / .7

z = 0.29

z = ( x - μ ) / σ

z = ( 9 - 6.8 ) / .7

z = 3.14

P ( 0.29 < z < 3.14) = 0.9992 - 0.6141 = 0.3851

38.51%

**Answer this Question**

**Related Questions**

Statistics (37) - According to the Sleep Foundation, the average night's sleep ...

statistics - researchers believe a new sleep on average 10 hours per night...

statistics - A 4 to 7 month old baby sleeps an average of 14 hours per day. At ...

statistics - A 4 to 7 month old baby sleeps an average of 14 hours per day. At ...

Probability/Statistics - Using diaries for many weeks, a study on the lifestyles...

statistics - The number of hours that college students sleep on a week night is...

statistics - College students average 7.8 hours of sleep per night with a ...

math - you got 8 hours of sleep on monday night and 7 hours of sleep on tuesday ...

Statistics - the average numbers of hours a cat sleep is approximately normally...

math - according to a recent survey 38% of americans get six hours or less of ...