Question

Based on historical data, your team knows what proportion of the company's orders come from Males (and Females). However, your team would like to expand its sales so that men are more proportionately represented. By the end of this year, you think you would like your total proportion of sales to males to be at least 0.45. If you took a simple random sample of 57 current orders, what is the probability that the sample proportion of male customers is greater than 0.45? Note: You should carefully round any intermediate calculations to 4 decimal places to match wamap's approach and calculations. Answer = Incorrect (Enter your answer as a number accurate to 4 decimal places.)

Gender	n	Mean	Variance	Std. dev.	Std. err.	Median	Range	Min	Max	Q1	Q3
Female	1404	110.26788	12292.386	110.87103	2.958929	73.95	796.68	4	800.68	32.755	150.16
Male	923	108.90898	12695.331	112.67356	3.7086953	72.15	868.45	4.04	872.49	31.62	149.11

Answer 1

Based on historical data, your team knows what proportion of the company's orders come from Males (and Females). However, your team would like to expand its sales so that men are more proportionately represented. By the end of this year, you think you would like your total proportion of sales to males to be at least 0.45. If you took a simple random sample of 57 current orders, what is the probability that the sample proportion of male customers is greater than 0.45? Note: You should carefully round any intermediate calculations to 4 decimal places to match wamap's approach and calculations. Answer = Incorrect (Enter your answer as a number accurate to 4 decimal places.) Gender   n   Mean   Variance   Std. dev.   Std. err.   Median   Range   Min   Max   Q1   Q3 Female   1404   110.26788   12292.386   110.87103   2.958929   73.95   796.68   4   800.68   32.755   150.16 Male   923   108.90898   12695.331   112.67356   3.7086953   72.15   868.45   4.04   872.49   31.62   149.11

The probability that the sample proportion of male customers is greater than 0.45 is 0.00003.

n = 2327

x = 923

p₀ = 923/2327

p₀ = 0.39665

By applying normal dsitribution:-

z = 4.28

P(z > 4.28) = 0.00003