To determine the probability of observing a certain number of successes, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where:
- P(X = k) is the probability of observing k successes
- n is the sample size
- k is the number of successes
- p is the proportion of successes in the population
In this case, n = 125, and p = 0.065.
A) To find the probability of observing 80 or fewer successes, we need to sum up the probabilities of observing 0, 1, 2, ..., 80 successes.
P(X ≤ 80) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 80)
B) To find the probability of observing 82 or fewer successes, we need to sum up the probabilities of observing 0, 1, 2, ..., 82 successes.
P(X ≤ 82) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 82)
C) To find the probability of observing 75 or more successes, we can subtract the probability of observing fewer than 75 successes from 1.
P(X ≥ 75) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 74))
To calculate each individual probability, we can use a calculator or statistical software.
A sample of 125 is drawn form population with proportion equal to .065 determine the probability of observing
A 80 or fewer successes
B 82 or fewer successes
C 75 or more fewer successes
1 answer