1. A study was done to compare the amount of time per day students at public and
ID: 3239620 • Letter: 1
Question
1. A study was done to compare the amount of time per day students at public and private universities spend on Facebook. The study was composed of 200 students from a private university and 300 students from a public university. The time that students at a private university spent on Facebook had a Normal distribution with a mean of 220 minutes and a standard deviation of 36 minutes. The time that students at a public university spent on Facebook had a Normal distribution with a mean of 200 minutes and standard deviation of 49 minutes. What is the distribution of the difference in times between students at a private university versus a public university?
A. N(20, 13)
B. N(420,13)
C. N(420,3697)
D. N(20,60.8)
2. A study was done to compare the amount of time per day students at public and private universities spend on Facebook. The study was composed of 200 students from a private university and 300 students from a public university. The time that students at a private university spent on Facebook had a Normal distribution with a mean of 220 minutes and a standard deviation of 36 minutes. The time that students at a public university spent on Facebook had a Normal distribution with a mean of 200 minutes and standard deviation of 49 minutes. What is the probability that students at a private university spend less time on Facebook than students at a public university?
A. .37
B. .63
C. 0
D. None of the above
3. Suppose X has the B(20, .5) distribution. The Normal approximation is ____ accurate because _______.
A. not; np 50 and n(1 - p) 50
B. very; p is close to .5, np 10, and n(1 - p) 10
C. very; the sample size is large
D. not; p is not close to 0 or 1
4. Suppose X has the B(20, .5) distribution. Using the Normal approximation for X with the continuity correction, calculate the P(X 10).
A. .5
B. .588
C. .412
D. None of the above
5. In a certain game of chance, your chances of winning are 0.2. Assume outcomes are independent and that you will play the game five times. What is the probability that you win at most once?
A. 0.4096
B. 0.0819
C. 0.7373
D. 0.2
Explanation / Answer
1)
X - private
Y - public
X - N(220,36^2)
Y - N(200,49^2)
X -Y - N(220 - 200 , 36^2 + 49^2)
N(20,3697)
N(20,60.8^2)
hence
optiona D) is correct
2)
P(X -Y < 0 ) Z = (X -mean)/sd = (X - 20)/60.8)
= P(Z < (0 - 20)/60.8) = 0.37
option A) is correct
3) np = 20 *0.5 = 10
n *(1-p) = 20*0.5 = 10
B) B. very; p is close to .5, np 10, and n(1 - p) 10
is correct by definition
4) E(X) = np = 20 *0.5 = 10
sd =sqrt(np*(1-p) = sqrt(20*0.5*0.5)= sqrt(5)
Z =(X -10)/sqrt(5)
P(X 10) = P(X< 9.5) due to contuinity correction
= P(Z <(10 -9.5)/sqrt(5)) =
P(Z< 0.22360)
= 0.5885
option B) is correct
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