Solution Found!
In 2003, the average combined SAT score (math and verbal)
Chapter 3, Problem 37E(choose chapter or problem)
Problem 37E
In 2003, the average combined SAT score (math and verbal) for college-bound students in the United States was 1026. Suppose that approximately 45% of all high school graduates took this test and that 100 high school graduates are randomly selected from among all high school grads in the United States. Which of the following random variables has a distribution that can be approximated by a binomial distribution? Whenever possible, give the values for n and p.
a The number of students who took the SAT
b The scores of the 100 students in the sample
c The number of students in the sample who scored above average on the SAT
d The amount of time required by each student to complete the SAT
e The number of female high school grads in the sample
Questions & Answers
QUESTION:
Problem 37E
In 2003, the average combined SAT score (math and verbal) for college-bound students in the United States was 1026. Suppose that approximately 45% of all high school graduates took this test and that 100 high school graduates are randomly selected from among all high school grads in the United States. Which of the following random variables has a distribution that can be approximated by a binomial distribution? Whenever possible, give the values for n and p.
a The number of students who took the SAT
b The scores of the 100 students in the sample
c The number of students in the sample who scored above average on the SAT
d The amount of time required by each student to complete the SAT
e The number of female high school grads in the sample
ANSWER:
Solution :
Step 1 of 5:
Given 52% of the population prefers to watch Jay Leno.
Let 3 late night watchers are randomly selected and asked which of the two talk show hosts they prefer.
Our goal is:
a). We need to find the probability distribution for Y, the number of viewers in the sample
prefer Leno.
b). We need to to construct a probability histogram for p(y).
c). We need to find the probability that exactly one of the three viewers prefers Leno.
d). We need to to calculate the mean and the Standard deviation.
e). We need to find the probability that the number of viewers favoring Leno falls within
2 Standard deviation of the mean.
a).
Now we have to find the probability distribution for Y, the number of viewers in the sample prefer Leno.
Here is the person prefer to watch Lenovo TV talk show is .
Here be the event.
Where i=0,1,2,3.
Then the probability of is
P()=52%
P()=0.52
Here is the person prefer to watch Lenovo TV talk show is .
Here be the event.
Where i=0,1,2,3.
The probability of is
P()= 1-P()
P()= 1-0.52
P()= 0.48
Let Y=0.
Let 3 late night watchers are randomly selected.
Here when all 3 viewers not prefer to watch the Lenovo show.
Then the probability of , is
or
p(0)=p(Y=0)
p(0)=
p(0)= 0.110592
p(1)=p(Y=1)
p(1)=
p(1)=
p(1)=
p(2)= p(Y=2)
p(2)=
p(2)=
p(2)= and
p(3)=p(Y=3)
p(3)=
p(3)= 0.140608
Therefore, p(0)= , p(1)=, p(2)= and p(3)= 0.140608.