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,

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 27% of ice cream sales
are vanilla. Chocolate accounts for only 7% of ice cream sales.
Suppose that 184 customers go to a grocery store in Cheyenne,
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cream sales. Suppose that 182 customers go to a grocery store in
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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 26% of ice
cream sales are vanilla. Chocolate accounts for only 13% of ice
cream sales. Suppose that 174 customers go to a grocery store in
Cheyenne, Wyoming, today to buy ice cream. (Round...

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 23% of ice cream sales
are vanilla. Chocolate accounts for only 12% of ice cream sales.
Suppose that 170 customers go to a grocery store in Cheyenne,
Wyoming, today to buy ice cream. (Round...

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 29% of ice
cream sales are vanilla. Chocolate accounts for only 8% of ice
cream sales. Suppose that 180 customers go to a grocery store in
Cheyenne, Wyoming, today to buy ice cream. (Round...

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 174 customers go to a grocery store in
Cheyenne, Wyoming, today to buy ice cream. (Round...

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 27% of ice cream sales
are vanilla. Chocolate accounts for only 8% of ice cream sales.
Suppose that 173 customers go to a grocery store in Cheyenne,
Wyoming, today to buy ice cream. (Round...

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 24% of ice cream sales
are vanilla. Chocolate accounts for only 12% of ice cream sales.
Suppose that 183 customers go to a grocery store in Cheyenne,
Wyoming, today to buy ice cream. (Round...

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 29% of ice
cream sales are vanilla. Chocolate accounts for only 14% of ice
cream sales. Suppose that 174 customers go to a grocery store in
Cheyenne, Wyoming, today to buy ice cream. (Round...

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 20% of ice cream sales
are vanilla. Chocolate accounts for only 12% of ice cream sales.
Suppose that 169 customers go to a grocery store in Cheyenne,
Wyoming, today to buy ice cream. (Round...

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