Question

Use technology​ (such as a binomial​ calculator) to find the probabilities shown below. Then determine if the events are unusual. Explain your reasoning. ​Sixty-eight percent of pet owners say they consider their pet to be their best friend. You randomly select 12 pet owners and ask them if they consider their pet to be their best friend. Find the probability that the number who say their pet is their best friend is​ (a) exactly nine​, ​(b) at least eight​, and​ (c) at most three.

Answer 1

Let the event of success be being a per owner with the probability p. Let X be the random variable which represents the successes in n attempts.

p = 0.68

n = 12

Unusually high event: x successes among n trials is an unusually high number of successes if P(x or more) ≤ 0.05.

Unusually low: x successes among n trials is an unusually low number of successes if P(x or fewer) ≤ 0.05.

We also know that,

P(X=x) = (nCx)*p^x*(1-p)^n-x

Using the above formula:

A.

P(X=9) = 0.2241

Since, P(X9) = 0.4319 > 0.05 i.e. it is not an unusual event

B.

P(X8) = 0.66923 > 0.05 i.e. it is not an unusual event

C.

P(X3) = 0.0028 < 0.05 i.e. it is an unusual event.

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