Question

Based on historical data, your manager believes that 44% of the company's orders come from first-time customers. A random sample of 59 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.33 and 0.49?

(Enter your answer as a number accurate to 4 decimal places.)

Answer 1

Given that Based on historical data, your manager believes that 44% of the company's orders come from first-time customers so the population prroportion is p = 0.44. A random sample of n = 59 orders will be used to estimate the proportion of first-time-customers.

To calculate that the probability that the sample proportion is between 0.33 and 0.49 P(0.33 < < 0.49) we need to check the requirement for assuming the distribution as normal that is:

n*p*(1-p) >=10 so, 59* 0.44*(1-0.44) = 14.54 thus the condition is satisfied, now the probability is calculted by finding the Z scores that is calculated as:

Thus the probability is calculated using the excel formula for normal distribution which is =NORM.S.DIST(0.77,TRUE)- NORM.S.DIST(-1.7, TRUE)

now the probability is computed as;