Concept explainers
Ice Cream: Flavors What’s your favorite ice cream flavor? For people who buy ice cream, the all-time favorite is still vanilla. About 25% of ice cream sales are vanilla. Chocolate accounts for only 9% of ice cream sales. (See reference in Problem 8.) Suppose that 175 customers go to a grocery store in Cheyenne. Wyoming, today to buy ice cream.
(a) What is the
(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
(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).
(a)
To find: The probability that 50 or more will buy vanilla.
Answer to Problem 14P
Solution: The probability that 50 or more will buy vanilla is
Explanation of Solution
Calculation: Using
Thus,
The condition
Now, we calculate
Now, mean and standard deviation are as follows:
Further, the z-value corresponding to x is
Thus, the desired probability is 0.1587.
(b)
To find: The probability that 12 or more will by chocolate.
Answer to Problem 14P
Solution: The probability that 12 or more will by chocolate is
Explanation of Solution
Calculation: The probability of sale one chocolate ice cream is
Using,
The condition
Now, we calculate
Now, mean and standard deviation are as follows:
Further, the z-value corresponding to x is
Thus, the desired probability is 0.8686.
(c)
To find: The probability that someone is buying any one flavor either vanilla or chocolate.
Answer to Problem 14P
Solution: probability that someone is buying any one flavor either vanilla or chocolate is 0.3175.
Explanation of Solution
Calculation: The probability that someone is buying any one flavor either vanilla or chocolate is
Let A represents vanilla flavor and B represents chocolate flavor.
Here, A and B are not mutually exclusive events and the choice to buy one flavor is independent of the choice to buy another flavor.
(d)
To find: The probability that between 50 and 60 customers will buy chocolate or vanilla ice-cream.
Answer to Problem 14P
Solution: The probability that between 50 and 60 customers will buy chocolate or vanilla ice-cream is
Explanation of Solution
Calculation: From part (c) the probability of buying chocolate or vanilla ice cream is
Now, we calculate
Now, mean and standard deviation are as follows:
Further,
Thus, the desired probability is 0.6246.
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Chapter 7 Solutions
Understanding Basic Statistics
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