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. 0.0000

b. 0.1841

c. 0.9992

Step-by-step explanation:

a. n = 285

p = 5% = 0.05

μ = np = 285 x 0.05

= 14.25

we fnd the standard deviation

sd = √np(1-p)

=
`√(285*0.05*0.95)`

= 3.6793

we find the z score

x = 30-0.5 = 29.5

`z=(29.5-14.25)/(3.6793) \\= 4.14`

using the microsoft excel function

1-NORMSDIST(4.14)

probability = 1 -0.999982

= 0.0000

b.

n = 502

p = 0.05

np = 502x0.05

= 25.1

sd =
`√(np(1-p))`

=
`√(502*0.05*0.95) \\= 4.8831`

x = 29.5

`z = (29.5-25.1)/(4.8831) \\= 0.90`

1 - NORMSDIST(0.90)

= 1 - 0.815939875

PROB = 0.1841

c. n = 1033

p = 0.05

np = 1033*0.05

= 51.65

sd
`√(np(1-p)) \\= √(1033*0.05*0.95)`

= 7.0048

x = 29.5

`z=(29.5-51.65)/(7.0048) \\= -3.16`

probability =

1 - normsdist(-3.16)

= 1 - 0.000788846

= 0.9992