78% of US homes have a telephone answering device. In a random sample of 250 homes, what is the probability that fewer than 50 do not have a telephone answering device. Courtney, 2nd yr college

To find the probability that fewer than 50 homes in the sample do not have a telephone answering device, we can use the binomial probability formula.

The binomial probability formula is given by:

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 success
(1-p) is the probability of failure
n is the total number of trials

In this case, we have n = 250 (the total number of homes in the sample), p = 0.78 (the probability that a home has a telephone answering device), and we want to find the probability that fewer than 50 homes do not have a telephone answering device.

To solve the problem, we need to find the cumulative probability from 0 to 49 (less than 50). We can do this by summing up the individual probabilities for k = 0 to 49 using the binomial probability formula.

P(X < 50) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 49)

Now, let's calculate the individual probabilities and sum them up to find the final probability.