Question

A sample of 125 is drawn form population with proportion equal to .065 determine the probability of success
A 80 or fewer successes
B 82 or fewer successes
C 75 or fewer successes

Answer 1

To determine the probability of success, we can use the binomial probability formula:

P(X = k) = (n C k) * p^k * (1-p)^(n-k)

Where:
n = sample size
k = number of successes
p = probability of success

A) 80 or fewer successes:
P(X ≤ 80) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 80)

n = 125
p = 0.065

Using the formula, we calculate the probability of each individual success and sum them up:

P(X ≤ 80) = sum[(n C k) * p^k * (1-p)^(n-k)], where k ranges from 0 to 80

B) 82 or fewer successes:
P(X ≤ 82) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 82)

We use the same formula, but this time we sum up the probabilities for k ranging from 0 to 82.

C) 75 or fewer successes:
P(X ≤ 75) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 75)

Again, we use the formula to sum up the probabilities for k ranging from 0 to 75.