(a)
To calculate: The
(a)
Answer to Problem 41E
The required probability is 0.0918.
Explanation of Solution
Given information:
Percent of orders = 90%
Number of orders = 5000
Number of orders for SRS = 100
Number of orders shipped in time = 86
Formula used:
The mean of the sampling distribution of
The standard deviation of the sampling distribution of
Calculation:
Here,
Find the mean of sampling distribution of
Substitute 86 for x and 100 for n in the above formula
For the mean of the sampling distribution of
Substitute 0.90 for p in the formula
For the standard deviation of the sampling distribution, use the formula
Substitute 0.90 for p and 100 for n in the above formula and simplify.
Now, we find the z-score by using the formula
Substitute 0.86 for
We can find the probability by using table A as:
Hence, the required probability is 0.0918.
(b)
The explanation that why the result of the sample does not refute the 90% claim.
(b)
Explanation of Solution
Given information:
Percent of orders = 90%
Number of orders = 5000
Number of orders for SRS = 100
Number of orders shipped in time = 86
Formula used:
The mean of the sampling distribution of
The standard deviation of the sampling distribution of
Here,
Find the mean of sampling distribution of
Substitute 86 for x and 100 for n in the above formula
For the mean of the sampling distribution of
Substitute 0.90 for p in the formula
For the standard deviation of the sampling distribution, use the formula
Substitute 0.90 for p and 100 for n in the above formula and simplify.
Now, we find the z-score by using the formula
Substitute 0.86 for
We can find the probability by using table A as:
Thus, the probability is 0.0918.
The above probability is greater than 0.05.
If the true population proportion is 0.90, then a sample can be obtained with sample proportion of 0.86 because the probability is greater than 0.05.
Hence, it is concluded that the result of the sample does not refute the 90% claim.
Chapter 7 Solutions
The Practice of Statistics for AP - 4th Edition
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