Question

1.In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

More than a decade ago, high levels of lead in the blood put 86% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 8% of children in the United States are at risk of high blood-lead levels.

(a) In a random sample of 216 children taken more than a decade ago, what is the probability that 50 or more had high blood-lead levels? (Round your answer to three decimal places.)


(b) In a random sample of 216 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)

2. In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Do you try to pad an insurance claim to cover your deductible? About 43% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 140 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.)

(a) half or more of the claims have been padded


(b) fewer than 45 of the claims have been padded


(c) from 40 to 64 of the claims have been padded


(d) more than 80 of the claims have not been padded

3. In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

What's your favorite ice cream flavor? For people who buy ice cream, the all-time favorite is still vanilla. About 30% of ice cream sales are vanilla. Chocolate accounts for only 13% of ice cream sales. Suppose that 181 customers go to a grocery store in Cheyenne, Wyoming, today to buy ice cream. (Round your answers to four decimal places.)

(a) What is the probability that 50 or more will buy vanilla?


(b) What is the probability that 12 or more will buy chocolate?


(c) A customer who buys ice cream is not limited to one container or one flavor. What is the probability that someone who is buying ice cream will buy chocolate or vanilla? Hint: Chocolate flavor and vanilla flavor are not mutually exclusive events. Assume that the choice to buy one flavor is independent of the choice to buy another flavor. Then use the multiplication rule for independent events, together with the addition rule for events that are not mutually exclusive, to compute the requested probability.


(d) What is the probability that between 50 and 60 customers will buy chocolate or vanilla ice cream? Hint: Use the probability of success computed in part (c).

Thank you so much!

Answer 1

Answer:

1.a)

Given,

sample n = 216

p = 0.86

Mean = np = 216 * 0.86 = 185.76 > 5

nq = 216*0.14 = 30.24 > 5

Condition satisfied

Standard deviation = sqrt(npq) = sqrt(216*0.86*0.14) = 5.10

P(X >= 50) = P(z > (50 - 185.76)/5.1)

= P(z > -26.62)

= 1 - P(z < -26.62)

= 1 - 0

= 1

b)

n = 216 , p = 0.08

Mean = np = 216*0.08 = 17.28 > 5

standard deviation = sqrt(npq) = sqrt(216*0.08*0.92) = 3.99

P(X >= 50) = P(z >= (50 - 17.28)/3.99)

= P(z > 8.2)

= 0

Please post the remaining questions as separate post. Thank you,