Concept explainers
(a)
To find: The probability that the sample proportion lies between 0.59 and 0.65.
(a)
Answer to Problem 71E
Solution: The probability that a randomly selected sample has proportion between 0.59 and 0.65 is 0.832.
Explanation of Solution
Calculation: The mean of the binomial distribution is calculated as.
The standard deviation
Also,
As
Now, obtain the Z-scores for
The Z score for
The Z score for
Now, calculate the probability that the sample proportion
By using the standard normal table, the areas corresponding to probabilities
So,
Hence, the required probability is 0.832.
(b)
To find: The probability that the sample proportion lies between 0.87 and 0.93.
(b)
Answer to Problem 71E
Solution: The probability that a randomly selected sample has proportion between 0.87 and 0.93 is 0.974.
Explanation of Solution
Calculation: The mean of the binomial distribution is calculated as.
The standard deviation
Also,
As
Now, obtain the Z scores for
The Z score for
The Z score for
Now, calculate the probability that the sample proportion
By using the standard normal table, the areas corresponding to probabilities
So,
Hence, the required probability is 0.975.
(c)
To explain: The effect on the probability of sample proportion
(c)
Answer to Problem 71E
Solution: As the value of true population proportion p goes closer to 1, the probability of sample proportion
Explanation of Solution
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Chapter 5 Solutions
Introduction to the Practice of Statistics
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