Question

About 5​% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees who earn the prevailing minimum wage or less. Complete parts​ (a) through​ (c) below. ​

(a) Company A has 285 employees. What is the probability that Company A will get the​ discount? ​(Round to four decimal places as​ needed.)

​(b) Company B has 502 employees. What is the probability that Company B will get the​ discount? ​(Round to four decimal places as​ needed.)

​(c) Company C has 1033 employees. What is the probability that Company C will get the​ discount? ​(Round to four decimal places as​ needed.)

Answer 1

(a)

Let X is a radnom variable shows the number of employees out of 285 earn the prevailing minimum wage or less.Here X has binomial distribution with parameters n=285 and p=0.05.

Since np and n(1-p) are greater than 5 so using normal approximation X has normal distribution with parameters

and standard deviation

here we need to use continuity correction. The z-score for X = 30-0.5 = 29.5 is

The probability that Company A will get the​ discount is

The excel function used for finding area right to z-score 4.14 is " =1-NORMSDIST(4.14)".

Answer: 0.0000

(b)

Let X is a radnom variable shows the number of employees out of 502 earn the prevailing minimum wage or less.Here X has binomial distribution with parameters n=502 and p=0.05.

Since np and n(1-p) are greater than 5 so using normal approximation X has normal distribution with parameters

and standard deviation

here we need to use continuity correction. The z-score for X = 30-0.5 = 29.5 is

The probability that Company B will get the​ discount is

The excel function used for finding area right to z-score 0.90 is " =1-NORMSDIST(0.90)".

Answer: 0.1841

(c)

Let X is a radnom variable shows the number of employees out of 1033 earn the prevailing minimum wage or less.Here X has binomial distribution with parameters n=1033 and p=0.05.

Since np and n(1-p) are greater than 5 so using normal approximation X has normal distribution with parameters

and standard deviation

here we need to use continuity correction. The z-score for X = 30-0.5 = 29.5 is

The probability that Company C will get the​ discount is

The excel function used for finding area right to z-score -3.16 is " =1-NORMSDIST(-3.16)".

Answer: 0.9992