Pregunta
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You may need to use the appropriate appendix table or technology to answer this question.
The president of Howahkan Distributors, Inc., believes that of the firm’s orders come from first-time customers. A
random sample of 100 orders will be used to estimate the proportion of first-time customers.
(a) Assume that the president is correct and . Describe the sampling distribution of for this study by specifying
its distribution form and parameters? (Round your answer for to four decimal places.)

(b) What is the probability that the sample proportion will be between 0.20 and 0.40 ? (Round your answer to four
decimal places.)
distribution – Select— ) appropriate in this case.
© What is the probability that the sample proportion will be between 0.25 and 0.35 ? (Round your answer to four
decimal places.)

Ask by Beck Bird. in the United States
Mar 16,2025

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(a) The sampling distribution of is approximately normal with and .
(b) The probability that is between 0.20 and 0.40 is approximately 0.9708.
© The probability that is between 0.25 and 0.35 is approximately 0.7242.

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The Deep Dive

The sampling distribution of is approximately normal because the sample size is large (n=100). Since we’re assuming , the expected value of is . The standard deviation of the sample proportion, , can be calculated using the formula:
So, and .
To find the probability that is between 0.20 and 0.40, we will need to standardize these values using the z-score formula:
Calculating for :
Calculating for :
Using standard normal distribution tables or technology, we can find:
Thus, the probability that the sample proportion will be between 0.20 and 0.40 is approximately 0.5110.
Now calculating for ©, we’ll find the probability that the sample proportion will be between 0.25 and 0.35.
For :
For :
Again using the standard normal distribution tables or technology:
Therefore, the probability that the sample proportion will be between 0.25 and 0.35 is approximately 0.2736.

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