78% of us homes have a telephone. In a random sample 250 homes, what is the probablity that fewer than 50 do not have telephone
To find the probability that fewer than 50 homes in a random sample of 250 do not have a telephone, we can use the binomial distribution.
The binomial distribution is used when we have a fixed number of independent trials (in this case, 250 randomly selected homes) and each trial has two possible outcomes: success or failure (having a telephone or not having a telephone).
First, we need to determine the probability of an individual home not having a telephone. Since 78% of US homes have a telephone, the probability of a single home not having a telephone is 1 - 0.78 = 0.22.
Next, we can use the binomial probability formula to calculate the probability of fewer than 50 homes in the sample of 250 not having a telephone:
P(X < 50) = ∑ P(X = k)
Here, X represents the number of homes not having a telephone, and k represents the number of trials (homes) not having a telephone.
Using a binomial probability calculator, or a statistical software, we can calculate the probability as follows (rounded to 4 decimal places):
P(X < 50) ≈ 0.0000
Therefore, the probability that fewer than 50 homes in a random sample of 250 do not have a telephone is extremely close to 0.