Question

Based on historical data, your manager believes that 42% of the company's orders come from first-time customers. A random sample of 85 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.36 and 0.47?

Answer 1

0.9560

Explanation:

Given that based on historical data, your manager believes that 42% of the company's orders come from first-time customers

Population proportion p = 0.42

Sample size n = 85

p is Normal with mean = 0.42 and std error =
`\sqrt{(p(1-p))/(n) } \\=0.0535`

p is N(0.42, 0.0535)

Or we can say
`(p-0.42)/(0.0535) =Z(0,1)`

the probability that the sample proportion is between 0.36 and 0.47

=
`P(0.36<X<0.47)\\= P(-1.12<z<0.94)\\\\=0.9560`