Total sleep time of college students. The total sleep time per night among colle
ID: 3173446 • Letter: T
Question
Total sleep time of college students. The total sleep time per night among college students was approximately Normally distributed with mean mu = 6.78 hours and standard deviation sigma = 1.24 hours. You plan to take an SRS of size n = 150 and compute the average total sleep time. What is the standard deviation for the average time? Use the 95 part of the 68-95-99.7 rule to describe the variability of this sample mean. What is the probability that your average will be below 6.9 hours? Number of friends on Facebook. Facebook recently examined all active Facebook users (more than 10% of the global population) and determined that the average user has 190 friends. This distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a median of 100 friends. Suppose that sigma = 288 and you take 7 an SRS of 70 Facebook users. For your sample, what are the mean and standard deviation of friends per user? the mean number of Use the central limit theorem to find the probability that the average number of friends for 70 Facebook users is greater than 250.Explanation / Answer
Given,
mean(µ)=6.78
SD(pop)=1.24
Sample size(n)=150
A.a) standard deviation = 1.24/sqrt(150)
standard deviation =0.1012
A.b) Sample mean(X)=6.78
at 68% confidence interval, the variability is 1 SD (X±1SD)
at 95% confidence interval, the variability is 2 SD (X±2SD)
at 99.7% confidence interval, the variability is 3 SD (X±3SD)
95% confidence interval
6.78±2*0.1012
6.78±0.2024
the confidence interval for 95% is given as (6.5776,6.9824)
A.c) P(X<6.9)
Z-staistic=6.9-6.78/0.1012
Z-statistic=1.19
from the table we get the probability as 0.5+0.3830 or 0.8830
hence the prob that average time will be below 6.9 hours is 88.3%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.