Question

The number of students taking the SAT has risen to an all-time high of more than 1.5 million The number of times the SAT was taken and the number of students are as follows.

Number of Times	Number of Students
1	797,000
2	645,000
3	125,000
4	26,000
5	26,200

a. Let x be a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable. Round your answers to four decimal places.

x	f(x)
1
2
3
4
5

b. What is the probability that a student takes the SAT more than one time? Round your answer to four decimal places.

c. What is the probability that a student takes the SAT three or more times? Round your answer to four decimal places.

d. What is the expected value of the number of times the SAT is taken? Round your interim calculations and final answer to four decimal places.

e. What is the variance and standard deviation for the number of times the SAT is taken? Round your interim calculations and final answer to four decimal places.

Variance
Standard deviation

Answer 1

SolutionA:

For x=1 prob=f(x)=797000/1619200=0.4922

For x=2,f(x)=645000/1619200=0.3983

for x=3,f(x)=125000/1619200=0.0772

for x=3,f(x)=26000/1619200=0.0161

for x=4,f(x)=26200/1619200=0.0162

x	f(x)
Times
1	0.4922
2	0.3983
3	0.0772
4	0.0161
5	0.0162

b. What is the probability that a student takes the SAT more than one time? Round your answer to four decimal places.

P(X=2)+P(X=3)+P(X=4)+P(X=5)

0.3983+0.0772+0.0161+0.0162
=0.5078

0.5078

c. What is the probability that a student takes the SAT three or more times? Round your answer to four decimal places.

P(X=3)+P(X=4)+P(X=5)

=0.0772+0.0161+0.0162

=0.1095

0.1095

d. What is the expected value of the number of times the SAT is taken?

expected value of the number of times the SAT is taken=mean of rvX

=1*0.4922+2*0.3983+3*0.0772+4*0.0161+5*0.0162

=1.6658

1.6658