Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

that on average, adults sleep 6.9 hours per night. Suppose that the standard dev

ID: 3355253 • Letter: T

Question

that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours a. Use Chebyshev's theorem to caloulate the percentage of individuals who sleep between 4.5 and 9.3 hours b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours c Assume that the number of hours of sleep folows a beli-chaped distibution Use the enpinical rule to caluilate the percentage of individuals who sleep between 4.5 and 9.3 hours per da 0% At least At least * % (Round to the nearest whole percentage.)

Explanation / Answer

Ans:

a)mean=6.9

std.dev=1.2

a)6.9-4.5=2.4=2*std. dev

9.3-6.9=3.6=2.4=2*std dev

k=2

1-(1/k^2)=1-(1/4)=3/4=0.75

At least 75%

b)6.9-3.9=3=2.5*std dev

9.9-6.9=3=2.5*std. dev

1-(1/k^2)=1-(1/2.5^2)=1-(1/6.25)=0.84

At least 84%

c)4.5 and 9.3 are two standard deviations away from mean.

According to empirical rule: 95% of the data will fall within two standard deviation of the mean.