Question

BINOMİAL PROBABnrTY ) The college bealth center did a survey Md fond thnt 20% of students mie agarettes. A group of 9 students randomly eit at the same table Fnd the a) Five studenta at the table smoks b) No student at the table smoke c) Les than 3 students at the table smoke AT'V commentator daime that 40% of all football injurien are knee injure. What is the probability that in a game with 5 reported injurien a) All are knee injuries b) At lenet three are knee injuries c) No more thah 2 are knee injurien The probability of an adverse reaction to a pneumonis shot is 0.10 Pheumonia shots are given to a group of 12 people. What is the probsbility that: a) Two ar fewer of 12 people have an advense reaction. b) None of them have an adverse reaction (4) The probability that a rentanrant patron will request seating in the outdoor patio is 0.40 A random sumple of 7 people call to make reservations Pind the probability that at most 2 of then reqoent outdoor seating b) Find the probability thai at leaet 5 of them request outdoor senting Sharon malm talphone appeal» fr danation1 she knows bom e prince that about 30% of the calle renult in dosations. If she maken 11 calls, what is the probability that ) she will get exactly 8 donations b)what i, tbe expected mimber of donation from iial? me owner of motel have noticed that in a long run about 40% of the people who top to inquire abogt room for the night actually rent a room a) I 12 people stop to incqaire about roome, fad the probability that at leaat 8 of them will reata b) Ir 25 emparate inquiries are madle about room, whad in the esxpected oumber of restaler onaming from inquires parate inquirim are macle Binomial Probability Formala Probsbility of x sacoms and (n-x) failures in n independent repested trinlsi P)Ce bare p is s proboabhility ofcc in a single trial (7) A mont report stated that 32% of lantiagin of driving "ge owned a ar. Coakler a random-angle of 7 teenngis. Find the probability that 5 of them do not own a car (B) It i. claimed that 72%ofthe ears are going fater than 65 milm per hour. Anadom mmple of 10 an wa oteerved. What is the probability that 8 of them were going faster than 65 miles per hour? (9) Is in estimated that 4 out of 5 patients murvive a risaky heart operation Of seven patients who recently had such operstion, what is the probability that all will narvive

Answer 1

1)

For a binomial distribution,

P(X=x) = ⁿC_x p^x (1-p)^n-x

p = 0.2

n = 9

a)

P(X=5) = ⁹C₅ 0.2⁵ (1-0.2)^9-5 = 0.0165 or 1.65%

b)

P(X=0) = ⁹C₀ 0.2⁰ (1-0.2)^9-0 = 0.1342 or 13.42%

c)

P(X<3) = P(X=0) + P(X=1) + P(X=2) = 0.7382 or 73.82%

2)

For a binomial distribution,

P(X=x) = ⁿC_x p^x (1-p)^n-x

p = 0.4

n = 5

a)

P(X=5) = ⁵C₅ 0.4⁵ (1-0.4)^5-5 = 0.0102 or 1.02%

b)

P(X>=3) = P(X=3) + P(X=4) + P(X=5) = 0.3174 or 31.74%

c)

P(X<=2) = 1-P(X>=3) =1- 0.3174 = 0.6828 or 68.28%

3)

For a binomial distribution,

P(X=x) = ⁿC_x p^x (1-p)^n-x

p = 0.1

n = 12

a)

P(X<=2) = P(X=0) + P(X=1) + P(X=2) = 0.8891 or 88.91%

b)

P(X=0) = ¹²C₀ 0.1⁰ (1-0.1)^12-0 = 0.2824 or 28.24%

5)

For a binomial distribution,

P(X=x) = ⁿC_x p^x (1-p)^n-x

p = 0.3

n = 11

a)

P(X=8) = ¹¹C₈ 0.3⁸ (1-0.3)^11-8 = 0.0037 or 0.37%

b)

We will calculate the probability for each value of X.

x	P(x)	x*P
0	0.019773	0
1	0.093217	0.093217
2	0.19975	0.399501
3	0.256822	0.770466
4	0.220133	0.880532
5	0.13208	0.660399
6	0.056606	0.339634
7	0.017328	0.121298
8	0.003713	0.029706
9	0.00053	0.004774
10	4.55E-05	0.000455
11	1.77E-06	1.95E-05
	Total	3.3

Expected Value = Mean = ∑px = 3.3

PS: We are only allowed to answer 4 parts per question