Question

Seventy-eight percent of workers say they work more than 45 hours per week. You randomly select 50 workers and ask if they work more than 45 hours per week.

1. What is the probability that exactly 36 workers say they work more than 45 hours per week?

Answer 1

The probability of exactly 36 out of 50 workers saying they work more than 45 hours per week can be calculated using the binomial probability formula. It involves computing combinations for n=50 and k=36, and then calculating the probability with the success rate of 0.78.

Step-by-step explanation:

The question asks for the probability that exactly 36 out of 50 workers say they work more than 45 hours per week, given that 78% report working more than 45 hours. To find this, we use the binomial probability formula:

P(X = k) = nCk * p^k * (1-p)^(n-k)

Where:

• n is the total number of trials (50 workers),
• k is the number of successful trials (36 workers),
• p is the probability of success (0.78), and
• nCk is the number of combinations of n items taken k at a time.

First, calculate nCk for n=50 and k=36:

nCk = 50! / (36! * (50-36)!)

Then, plug that into the formula along with p and calculate the probability:

P(X = 36) = (50C36) * (0.78)^36 * (1-0.78)^(50-36)

This formula will give the probability that exactly 36 workers say they work more than 45 hours per week. Calculating it requires the use of a calculator or computer software capable of handling binomial probabilities.