Question
Based on historical data, your manager believes that 33% of the company's orders come from first-time...
Based on historical data, your manager believes that 33% of the company's orders come from first-time customers. A random sample of 245 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.22 and 0.39? (Enter your answer as a number accurate to 4 decimal places.)
Homework Answers
Answer #1
Solution :
Given that ,
p = 0.33
1 - p = 0.67
n = 245
= p = 0.33
= 
(p*(1-p))/n = (0.33*0.67)/
245= 0.03004
P(0.22 < 
< 0.39 ) = P((0.22 - 0.33)/0.03004 ) < (
-
) / <
(0.39 - 0.33) /0.03004 ) )
= P(-3.662 < z < 1.997 )
= P(z < 1.997) - P(z < -3.662)
= 0.9771 - 0.0001
= 0.9770
Probability = 0.9770
The probability that the sample proportion is between 0.22 and 0.39 is 0.9770.
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