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
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.
To determine the probability of observing the given number of successes, we can use the binomial distribution. The formula for the probability of x successes in a binomial distribution is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
Where:
- n is the sample size
- x is the number of successes
- p is the proportion of successes in the population
For the given sample size of 125 and a population proportion of 0.065, we can calculate the probabilities as follows:
A) 80 or fewer successes:
P(x ≤ 80) = P(x=0) + P(x=1) + P(x=2) + ... + P(x=80)
B) 82 or fewer successes:
P(x ≤ 82) = P(x=0) + P(x=1) + P(x=2) + ... + P(x=82)
C) 75 or more successes:
P(x ≥ 75) = 1 - P(x=0) - P(x=1) - P(x=2) - ... - P(x=74)
To calculate these probabilities, we need to know the values of n, x, and p. However, it appears that the values of n, x, and p are missing in your question. Please provide the missing values so that I can calculate the probabilities accurately for you.