Question

Q2. According to a Bon Appetit poll, 38% of people prefer chocolate ice cream. Use the binomial formula for calculating probabilities in a., b. and (ii).

(i) If 10 people are chosen at random, a. What is the probability that none prefer chocolate ice cream? b. What is the probability that only one prefers chocolate ice cream? c. What is the probability that more than one prefer chocolate ice cream? d. What is the expected number that prefer chocolate ice cream?

(ii) If 22 people are chosen at random, what is the probability that exactly 11 prefer chocolate ice cream?

Answer 1

i).X: number of people who prefer chocolate ice cream.

X ~ bin (n,p)

where, n= 10

p = 38% = 0.38

q = (1-p) = (1-0.38) = 0.62

the pmf of the distribution be:-

a). the probability that none prefer chocolate ice cream be:-

b). the probability that only one prefer chocolate ice cream be:-

c). the probability that more than one prefer chocolate ice cream be:-

d).the expected number that prefer chocolate ice cream be:-

ii).X: number of people who prefer chocolate ice cream.

X ~ bin (n,p)

where, n= 22

p = 38% = 0.38

q = (1-p) = (1-0.38) = 0.62

the pmf of the distribution be:-

the probability that exactly 11 will prefer chocolate ice cream be:-

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