Question

Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 122 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.21?

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

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

Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 138 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 0.35?

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

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

Answer 1

Solution

Given that,

1) p = 34% = 0.34

1 - p = 1 - 0.34 = 0.66

n = 122

= p = 0.34

=  [p( 1 - p ) / n] = [(0.34 * 0.66) / 122 ] = 0.0429

P( > 0.21) = 1 - P( < 0.21)

= 1 - P(( - ) / < ( 0.21 - 0.34) / 0.0429)

= 1 - P(z < -3.03 )

Using z table

= 1 - 0.0012

= 0.9988

2) Given that,

p = 32% = 0.32

1 - p = 1 - 0.32 = 0.68

n = 138

= p = 0.32

=  [p ( 1 - p ) / n] = [(0.32 * 0.68) / 138 ] = 0.0397

P( 0.21 < < 0.35 )

= P[( 0.21 - 0.32 ) / 0.0397 < ( - ) / < ( 0.35 - 0.32 ) / 0.0397 ]

= P( -2.77 < z < 0.76 )

= P(z < 0.76) - P(z < -2.77)

Using z table

= 0.7764 - 0.0028

= 0.7736