Question

A market research firm conducts telephone surveys with a 44% historical response rate. what is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? in other words, what is the probability that the sample proportion will be at least 150/400 = .375? calculate the probability to 4 decimals.

Answer 1

To calculate the probability that at least 150 individuals will cooperate and respond to the questions in a new sample of 400 telephone numbers with a historical response rate of 44%, we use the binomial distribution formula.

Step-by-step explanation:

To calculate the probability that at least 150 individuals will cooperate and respond to the questions, we need to use the binomial distribution formula. The formula is:

P(X ≥ k) = 1 - P(X

Where n is the sample size, k is the desired number of successes, p is the historical response rate, q = 1 - p is the failure rate.

In this case, n = 400, k = 150, p = 0.44, q = 1 - 0.44 = 0.56. Plugging these values into the formula, we get:

P(X ≥ 150) = 1 - P(X<150)

We can use a software or calculator to evaluate this expression. The probability is approximately 0.9328 to 4 decimal places.

Answer 2

EXAMPLE: A common source of frame error is the use of a telephone directory as a sampling frame for a telephone survey. Many houses are not liste