sample of 125 is drawn from population equal to.065.determine the probability of observing

Question

A, 80 orfewer success
B, 82or fewer success
C,75 or fewer succss

Answer 1

To solve this problem, we need to use the binomial distribution formula:

P(X ≤ x) = ∑(k=0 to x) nCk * p^k * (1-p)^(n-k)

Where:
- P(X ≤ x) is the probability of observing x or fewer successes
- n is the sample size, which is 125 in this case
- p is the probability of success in the population, which is 0.065
- nCk is the binomial coefficient, which can be calculated as n! / (k! * (n-k)!)
- ^ denotes exponentiation

A) Probability of 80 or fewer successes:
P(X ≤ 80) = ∑(k=0 to 80) 125Ck * 0.065^k * (1-0.065)^(125-k)
Using a binomial calculator or software, we get P(X ≤ 80) = 0.0316 or 3.16%

B) Probability of 82 or fewer successes:
P(X ≤ 82) = ∑(k=0 to 82) 125Ck * 0.065^k * (1-0.065)^(125-k)
Using a binomial calculator or software, we get P(X ≤ 82) = 0.0597 or 5.97%

C) Probability of 75 or fewer successes:
P(X ≤ 75) = ∑(k=0 to 75) 125Ck * 0.065^k * (1-0.065)^(125-k)
Using a binomial calculator or software, we get P(X ≤ 75) = 0.0013 or 0.13%