Question

Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 152 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.31?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer =

Answer 1

Solution :

Given that ,

p = 0.32

1 - p = 0.68

n = 152

= p = 0.32

= (p*(1-p))/n =  (0.32*0.52)/ 152= 0.03784

P( <0. 31) = P(( - ) / < (0.31 - 0.32) / 0.03784)

= P(z < -0.26)

= 0.3974 Using z-table,

The probability that the sample proportion is less than 0.31 is 0.3974