Question

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.

Ocean fishing for billfish is very popular in the Cozumel region of
Mexico. In the Cozumel region about 41% of strikes (while trolling)
resulted in a catch. Suppose that on a given day a fleet of fishing
boats got a total of 26 strikes. Find the following probabilities.
(Round your answers to four decimal places.)

(a) 12 or fewer fish were caught

(b) 5 or more fish were caught

(c) between 5 and 12 fish were caught

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.

It is known that 80% of all new products introduced in grocery
stores fail (are taken off the market) within 2 years. If a grocery
store chain introduces 65 new products, find the following
probabilities. (Round your answers to four decimal places.)

(a) within 2 years 47 or more fail

(b) within 2 years 58 or fewer fail

(c) within 2 years 15 or more succeed

(d) within 2 years fewer than 10 succeed

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 10% of ice
cream sales. Suppose that 182 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).

Answer #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. 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,
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 28% of ice
cream sales are vanilla. Chocolate accounts for only 14% of ice
cream sales. Suppose that 182 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 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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