Final answer:
To find the probability of exactly 55 small business owners not having a college degree out of a random sample of 70, we can use the binomial distribution formula.
Step-by-step explanation:
To find the probability of exactly 55 small business owners not having a college degree, we can use the binomial distribution formula. The formula is:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k successes
- C(n,k) is the number of combinations of n items taken k at a time
- p is the probability of a single success (in this case, the probability that a small business owner does not have a college degree)
- n is the number of trials (in this case, the sample size of 70)
In this case, p = 0.76 (since 76% of small business owners do not have a college degree) and n = 70. We want to find P(X=55), so k = 55.
Plugging in these values into the formula, we get:
P(X=55) = C(70,55) * 0.76^55 * (1-0.76)^(70-55)
Calculating this probability will give us the answer.