Questions: Assume that when human resource managers are randomly selected, 61% say job applicants should follow up within two weeks. If 30 human resource managers are randomly selected, find the probability that exactly 22 of them say job applicants should follow up within two weeks.

Assume that when human resource managers are randomly selected, 61% say job applicants should follow up within two weeks. If 30 human resource managers are randomly selected, find the probability that exactly 22 of them say job applicants should follow up within two weeks.

Transcript text: Assume that when human resource managers are randomly selected, $61 \%$ say job applicants should follow up within two weeks. If 30 human resource managers are randomly selected, find the probability that exactly 22 of them say job applicants should follow up within two weeks.

Solution

Solution Steps

Step 1: Understanding the Problem

We need to find the probability of observing exactly 22 successes in 30 trials, where the probability of success in a single trial is 0.61.

Step 2: Applying the Binomial Probability Formula for 'Exactly 22 Successes'

The formula to calculate this is: $$P(X = 22) = \binom{n}{k} p^k (1-p)^{n-k}$$

Step 3: Calculation

The calculation involves determining the binomial coefficient \(\binom{n}{k}\) and then using the binomial probability formula.

Final Answer:

The probability of exactly 22 successes in 30 trials is approximately 0.0593.

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