SOLUTION: Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 113 orders will be used to estimate the proporti

Question 1073291: Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 113 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.15?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Can use the normal approximation to this binomial.
np=mean which historically would be 38.42
np(1-p) is variance or 25.3572; sqrt is sd=5.036
a proportion of 0.15 represents 16.95
So z>=(16.95-38.42)/5.036=-4.26, which is about 100%.
------------------
z>(0.15-0.34)/sqrt((0.34*0.66)/113)=-0.19/0.0446, which is z>-4.26
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