Economics (37)
posted by Mia .
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)?
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)?

37) 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) = 10.9564 = 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% 
fe
Respond to this Question
Similar Questions

math
you got 8 hours of sleep on monday night and 7 hours of sleep on tuesday night on wednesday you only got 4 hours of sleep because you were up late working on an english paper on thursday and friday you got 9 hours of sleep each night … 
Probability/Statistics
Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found … 
statistics
College students average 7.8 hours of sleep per night with a standard deviation of 45 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 9 hours? 
statistics
researchers believe a new sleep on average 10 hours per night ( ยต = 10), with a population standard deviation of 2.3 hours(s=2.3) it is assume that the number of hours of sleep per night is normal distributed , however you think this … 
math
according to a recent survey 38% of americans get six hours or less of sleep each night. if 75 people are selected to participate in a sleep survey, find the probability that 30 or more of them get six hours of sleep each night 
Statistics
the average numbers of hours a cat sleep is approximately normally distributed with a mean of 15 hours and a standard deviation of 1.7 hours; what percentage of cats sleep between 13 and 18 hours 
Statistics (37)
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 … 
statistics
The number of hours that college students sleep on a week night is approximated by a normal curve with a mean of 7 hours and a standard deviation of 1.7 hours. Answer the question below using a z table: On a week night, what percentage … 
statistics
A 4 to 7 month old baby sleeps an average of 14 hours per day. At this age, babies sleep patterns follow normal distribution with the standard deviation of 1.6 a) is it unusual for a baby to sleep under 12 hours aday? 
statistics
A 4 to 7 month old baby sleeps an average of 14 hours per day. At this age, babies sleep patterns follow normal distribution with the standard deviation of 1.6 a) is it unusual for a baby to sleep under 12 hours a day?