SOLUTION: Based on historical data, your manager believes that 28% of the company's orders come from first-time customers. A random sample of 167 orders will be used to estimate the proporti
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Question 1147979: Based on historical data, your manager believes that 28% of the company's orders come from first-time customers. A random sample of 167 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.24 and 0.37?
Answer = (Enter your answer as a number accurate to 4 decimal places.)
You can put this solution on YOUR website! 0.28 is the population mean which is also the sample mean
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standard error of the proportion = square root( (0.28) * (1-0.28) / 167 ) = 0.0347
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since the sample size is > 30, the normal distribution can be used
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z-score(0.24) = (0.24 -0.28)/0.0347 is approximately -1.15
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z-score(0.37) = (0.37 -0.28)/0.0347 is approximately 2.59
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find the associated probabilities(P) in the table of z-scores
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P (X < 0.37) = 0.9952 and P(X < 0.24) = 0.1251
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P ( 0.24 < X < 0.37 ) = 0.9952 - 0.1251 = 0.8701
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