1. 8.1 Binomial Distribution
Homework Review

2. 8.4: GUESSING ON A TRUE-FALSE QUIZ
Since True false … p = .5 … n = 50
(a) P(X  25)
= 1 - P(X < 25) = 1 - P(X  24) = 1 – binomcdf (50, .5, 24) =
(b) P(X  30)
= 1 - P(X < 30) = 1 - P(X  29) = 1 – binomcdf (50, .5, 29) =
(c) P(X  32)
= 1 - P(X < 32) = 1 - P(X  31) = 1 – binomcdf (50, .5, 31) =

3. 8.6: DAD’S IN THE POKEY Since 2% behind bars … p = .02 … n = 100
(a) Satisfy Requirements?
F: N = 100; I: Each kid is independent; S: Each kid has same probability of .02; T: In pokey or not
(b) P(X = 0)
What is the probability that exactly none of the kids in the sample of 100 will have a father in prison
P(X = 0) = binompdf(100,.02,0) =
P(X = 1) = binompdf(100,.02,1) =
(c) P(X  2)
= 1 - P(X < 2) = 1 - P(X  1) = 1 – binomcdf (100, .02, 1) = =1-[ P(X = 0) + P(X = 1)] = =

4. 8.8: MARITAL STATUS
25% of women never have been married … 10 random women are chosen
(a) n? p?
p = .25 … n = 10
(b) P ( “ Exactly 2 ” )
P(X = 2) = binompdf (10, .25, 2) =
(c) P( “ 2 or fewer ” )
P(X  2) = binomcdf (10, .25, 2) =

5. 8.10: BROCCOLI PLANTS About 5% of broccoli plants die. You purchase 10
(a) Use binomial formula to find P( “you lose at most one of the plants”)
P(X  1) = P(X = 0) + P(X = 1)
0.9139

6. 8.12: GRADUATION RATES
The number of athletes that graduate is given by B(20, .8)
Use the binomial formula to find P( “that all 20 graduate”)
P(X = 20) =
Find P( “not all 20 graduate”)
P(X < 20) = 1- P(X = 20) =
0.0115
= .9885

7. 8.14: CORINNE’S FREE THROWS
The number of made shots that Corrine makes is given by B(12, .75)
Use the binomial formula to find P( “she makes exactly 7”)
P(X = 7) =
0.1032

8. 8.16: HISPANIC COMMITTEE MEMBERS
n = 15; p = .03
(a) What is the mean number of Hispanics?
E(X) = np = (15)(.03) = .45
(b)
Standard Deviation?
(c)
Standard Deviation? p = .1; p = .01
Notice that as the p-value get closer to zero, the standard deviation also gets smaller.
0.6607
1.1619
0.3854

9. 8.18: MARITAL STATUS OF EMPLOYEED WOMEN
n = 10; p = .25
(a) What is the mean number of Employed Women?
E(X) = np = (10)(.25) = 2.5
(b) Standard Deviation?
1.3693

10. 8.20: MARKET RESEARCH SURVEY
n = 200; p = .4
(a) Is a binomial distribution reasonable?
F: N = 200 in survey; I: Each resident is independent; S: Same probability of . Each time since random; T: Either seek nutritious or not
(b) What is the mean number and standard deviation of people who seek nutritious food?
E(X) = np = (200)(.4) = 80
(c) P(75 < X < 85) =
Rule of thumb: np = (200)(.4) = 80; nq = (200)(.6) = 12
6.9282

11. 75 85 80
Z=(85-80)/ = .7217
Normcdf (-.7217, .7217) = .5295