Question

12. In the US, 28% of people consider snickerdoodle as their favorite cookie. You asked 5 people if their favorite cookie was snickerdoodle. Create the probability distribution for the possible outcomes.

Answer 1

Given sample size n-5 people Probability ofpeople consider snickerdoodle as their favorite p=28% = 0.28 Let X be number of people consider follows binomial distribution with parameters n-5 and p-0.28 a) Probability of exactly 0 P (X-0) P (X-0) 5Co (0.28)(0.72)50 0.1935 b) Probability of exactly 1 P (X-1) P(X-1 C1 (0.28) (0.725-1 0.3762 c) Probability of exactly 2 P (X-2) P CX2) 5C2 (0.28) (0.72)5-2 0.2926 d) Probability of exactly 3 P (X-3) PC-3) = 5C3 (028)3(0.72)5-3 = 0.1138 e) Probability of exactly 4 P (X-4) P (X-4) 5C4 (0.28 (0.72)54 0.0221 Probability of exactly 5-P (X=5) P (X-55Cs(0.28) (0.72)5-5 0.0017 f)

The probability distribution is as follows POx) 0.1935 0.3762 0.2926 0.1138 0.0221 0.0017 eh 3