Question

Suppose that the proportion of cats returned after being adopted from a shelter is normally distributed....

Suppose that the proportion of cats returned after being adopted from a shelter is normally distributed. Past data indicates that the proportion of cats returned after being adopted is 10%. If a local shelter has adopted out 175 cats find the probability that 12 or more cats will be returned by answering the following questions.

(a) What is the sample size?

(b)What is the sample proportion?

(c) Calculate the z-score for the sample proportion

(d) Find the probability that 12 or more cats will be returned

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

(a) What is the sample size?

Answer: Sample size = n = 175

(b)What is the sample proportion?

Answer: Sample proportion = x/n = 12/175 = 0.068571

(c) Calculate the z-score for the sample proportion

Answer:

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.068571 - 0.10)/sqrt(0.10*0.90/175)

Z = -1.38589

(d) Find the probability that 12 or more cats will be returned

Here, we have to find P(X≥12) = P(Z>-1.38589) = 1 – P(Z<-1.38589) = 1 - 0.08289 = 0.91711

Required probability = 0.91711

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