Question

According to a government statistical organization, the unemployment rate for workers aged 23 to 27 in April 2018 was 6.5% Consider a random sample of 140 workers from this age group a. What is the probability that 8 or fewer will be unemployed? b. What is the probability that 4 or fewer will be unemployed? c. What is the probability that between 4 and 12 of them will be unemployed? 52

Answer 1

a. The probability of finding 8 or fewer unemployed workers in the sample is approximately 82.95%.

b. The probability of finding 4 or fewer unemployed workers in the sample is approximately 43.77%.

c. The probability of finding between 4 and 12 unemployed workers in the sample is approximately 85.87%.

a) Probability of 8 or fewer unemployed:

We can model the number of unemployed workers in the sample using a binomial probability distribution. In this case:

n = 140 (sample size)

p = 0.065 (unemployment rate)

x ≤ 8 (desired number of unemployed)

Using a binomial probability calculator or statistical software, we find the probability:

P(X ≤ 8) ≈ 0.8295

Therefore, the probability of finding 8 or fewer unemployed workers in the sample is approximately 82.95%.

b) Probability of 4 or fewer unemployed:

Similarly, using the same parameters but changing the desired number of unemployed:

x ≤ 4

P(X ≤ 4) ≈ 0.4377

The probability of finding 4 or fewer unemployed workers in the sample is approximately 43.77%.

c) Probability of 4 to 12 unemployed:

This requires calculating the probability of each individual case (5, 6, 7, 8, 9, 10, 11, and 12 unemployed) and then summing them up:

P(4 ≤ X ≤ 12) = P(X = 4) + P(X = 5) + ... + P(X = 12)

Using the binomial probability calculator for each x value and then adding them up, we get:

P(4 ≤ X ≤ 12) ≈ 0.8587

Therefore, the probability of finding between 4 and 12 unemployed workers in the sample is approximately 85.87%.