Question
In: Statistics and Probability
Based on historical data, your manager believes that 30% of the company's orders come from first-time...
Based on historical data, your manager believes that 30% of the company's orders come from first-time customers. A random sample of 77 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.34 and 0.47?
Solutions
Expert Solution
Solution:
Given that,
n = 77
= 30% =0.30
1 - 
= 1 - 0.30 = 0.70
=
= 0.30
= 
( 1 -
) / n
=
= 0.0522
= 0.0522
p ( 0.34 <
< 0.47 )
p ( 0.34 - 0.30 / 0.0522 ) < (
-
/
) < ( 0.47 - 0.30 / 0.0522 )
p (0.04 / 0.0522 < z < 0.17 / 0.0522 )
p ( 0.77 < z < 3.26 )
p ( z < 3.26 ) - p ( z < 0.77 )
Using z table
= 0.9994 - 0.7794
= 0.2200
Probability = 0.2200
orchestra answered 1 year agoRelated Solutions
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