Concept explainers
(a)
To explain: The accuracy of the
(a)

Answer to Problem 15.41E
The probability obtained in part (b) of Exercise 15.39 using normal approximation is under estimated compared with exact answer.
Explanation of Solution
Given info:
The probability that the Joe’s average winnings between 0.5 and 0.7 is 0.4961. The number of bets is 14,000.
Justification:
Here, the exact probability that the Joe’s average winning between 0.5 and 0.7 is 0.4961. From the part (b) of Exercise 15.39 using normal approximation the Joe’s average winnings is between 0.5 and 0.7 is 0.4648.
From the above two probabilities, it can be observed that the probability obtained by using normal approximation is less than the exact probability. Thus, the probability obtained in part (b) of Exercise 15.39 by using normal approximation is under estimated.
(b)
To explain: The accuracy of the probability of
(b)

Answer to Problem 15.41E
The probability of
Explanation of Solution
Given info:
The data shows that the probability that the Joe’s average winnings are between 0.5 and 0.7 is 0.4048. The number of bets is 3,500.
Calculation:
From the part (a) of the Exercise 15.39 the population
Central limit theorem:
It states that as the
Mean of the Sampling distribution of
The sample mean
Standard deviation of the Sampling distribution of
The standard deviation can be calculated by using the formula
Substitute 18.96 for
Thus, the standard deviation of
Probability using normal approximation:
Thus, the probability of
From the given problem the probability that the Joe’s average winnings are between 0.5 and 0.7 is 0.4048. From the above results it can be observed that probability 0.4048 is greater than 0.2434.
Hence, the probability of
(c)
To explain: The accuracy of the probability of
(c)

Answer to Problem 15.41E
The probability of
Explanation of Solution
Given info:
The data shows that the probability that the Joe’s average winnings are between 0.5 and 0.7 is 0.9629. The number of bets is 150,000.
Calculation:
Mean of the Sampling distribution of
The sample mean
Standard deviation of the Sampling distribution of
The standard deviation can be calculated by using the formula
Substitute 18.96 for
Thus, the standard deviation of
Probability using normal approximation:
Thus, the probability of
From the given problem the probability that the Joe’s average winnings are between 0.5 and 0.7 is 0.9629. From the above results it can be observed that probability 0.9586 is less than 0.9629.
Hence, the probability of
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Chapter 15 Solutions
BASIC PRACTICE OF STATISTICS >C<
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