The probabilities for various binomial distribution have been determined.
The complete question is
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.)
<h3>What is Probability ?</h3>
Probability is a stream in mathematics that study the likeliness of an event to happen .
On the basis of the given data
(a) Let X is a random variable that denotes the number of employees that earn less than prevailing average.
Here X has binomial distribution with
n=285 and p=0.05.
As np and n(1-p) are greater than 5 so using normal approximation X has normal distribution with parameters
μ= np-285 * 0.05
= 14.25
standard deviation is given by

Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is

The probability that Company A will get the discount is given by

(b) Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with
n=502 and p=0.05.

standard deviation

Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is

The probability that Company B will get the discount is

(c)Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with
n=1033 and p=0.05.

standard deviation

Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is

The probability that Company C will get the discount is

Therefore the probabilities for various binomial distribution have been determined.
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