Question

Based on historical data, your manager believes that 33% of the company's orders come from first-time customers. A random sample of 102 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.27? Note: You should carefully round any z-values you calculate to 4 decimal places.

Answer =

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

Answer 1

Solution:

Given that,

n = 102

= 33% =0.33

1 - = 1 - 0.330 = 0.67

=   = 0.33

= ( 1 - ) / n

=   0.33 * 0.67 / 102

= 0.0116

=0.0465

p (   < 0.27 )

p ( -    / ) < ( 0.27 - 0.33 / 0.0465 )

p ( z < - 0.06 / 0.0465 )

Using z table

p ( z < -1.2903 )

= 0.0985

Proportion  = 0.0985