Based on historical data, your manager believes that 35% of

Lucille Smitherman

Lucille Smitherman

Answered question

2021-12-02

Based on historical data, your manager believes that 35% of the company's orders come from first-time customers. A random sample of 175 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.21 and 0.39?

Answer & Explanation

Charles Wee

Charles Wee

Beginner2021-12-03Added 14 answers

Step 1
Given information:
p=35100
=0.35
n=175
p1=0.21
By applying normal distribution:
z=p^pp(1p)n
=0.210.350.35(10.35)175
=0.140.03606
=3.88
z1=3.88
Step 2
p2=0.39
By applying normal distribution:
z=p^pp(1p)n
=0.390.350.35(10.35)175
=0.040.03606
=1.11
z2=1.11
P(3.88<z<1.11)=P(z<1.11)P(z<3.88)
Use the excel formula, "=NORM.S.DIST(1.11,TRUE)" and "=NORM.S.DIST(-3.88,TRUE)" for determining the p-values.
P(3.88<z<1.11)=0.866500.00005
P(3.88<z<1.11)=0.86645
The probability that the sample proportion is between 0.21 and 0.39 is 0.8665.

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