In his management information systems textbook,Professor David Kroenke raises and interesting point:"If 98% of our market has Internet access,do we have a responsibility to provide non-Internet materials to that other 2%?Suppose that 98% of the customers in your market have Internet access,and you select a random sample of 500 customers.What is the probablity that the sample has

a.greater than 99% of the customers with internet access?
b..between 97% and 99% of the customers with internet access?
c.fewer than 97% of the customers with Internet access?

To answer these questions, we need to use the concept of the binomial distribution. The binomial distribution is used to model the number of successes in a fixed number of independent Bernoulli trials.

Let's define the following variables:
- n = sample size = 500
- p = probability of success (customers with internet access) = 0.98
- q = probability of failure (customers without internet access) = 1 - p = 0.02

We can now calculate the probabilities:

a. To find the probability that the sample has greater than 99% of the customers with internet access, we need to calculate the cumulative probability for successes starting from 99%

P(X > 99%) = P(X ≥ 495)

Using the binomial distribution:

P(X = k) = nCk * p^k * q^(n-k)

P(X ≥ 495) = P(X = 495) + P(X = 496) + ... + P(X = 500)

Using a statistical calculator or software, we can calculate this probability.

b. To find the probability that the sample has between 97% and 99% of the customers with internet access, we need to calculate the cumulative probability for successes between 97% and 99%.

P(97% ≤ X ≤ 99%) = P(X ≥ 485) - P(X ≥ 495)

Again, we can use a calculator or software to calculate this probability.

c. To find the probability that the sample has fewer than 97% of the customers with internet access, we need to calculate the cumulative probability for successes less than 97%.

P(X < 97%) = P(X ≤ 484)

Using a calculator or software, we can calculate this probability as well.

Please note that the exact calculations require statistical software or a calculator with binomial probability functions.

To solve this problem, we need to use the concept of probability. We can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.

Let's start by determining the favorable outcomes for each part of the question:

a. Greater than 99% of the customers with Internet access:
So, we need to find the probability that more than 99% of the customers in the sample have Internet access. Since 98% of the market has Internet access, any value greater than 99% would fall into this category.

To calculate this probability, we will use the concept of a binomial distribution. In a binomial distribution, we have a fixed number of independent trials, each with the same probability of success. In this case, we have a sample of 500 customers, and each customer either has or doesn't have Internet access.

To calculate the probability, we need to use the binomial probability formula:

P(X > k) = 1 - P(X <= k)

Where P(X > k) is the probability of getting more than k successes, and P(X <= k) is the probability of getting k or fewer successes.

In this case, P(X <= k) can be calculated using the cumulative binomial probability formula:

P(X <= k) = ∑(j=0 to k) [nCj * p^j * (1-p)^(n-j)]

Where nCj is the combination formula (n choose j), p is the probability of success (98% or 0.98 in this case), and n is the number of trials (500 in this case).

Using this formula, we can calculate the probability of getting more than 99% of customers with Internet access by subtracting the probability of getting 99% or fewer customers with Internet access from 1.

b. Between 97% and 99% of the customers with Internet access:
In this case, we need to find the probability that the sample has between 97% and 99% of customers with Internet access. We can calculate this by finding the difference between the probabilities of getting 97% or fewer and the probabilities of getting 99% or fewer, since these cover the desired range.

c. Fewer than 97% of the customers with Internet access:
Here, we need to find the probability that the sample has fewer than 97% of customers with Internet access. This can be calculated by finding the probability of getting 96% or fewer customers with Internet access.

To summarize, we need to calculate the probabilities using the binomial probability formula and cumulative binomial probability formula for parts a, b, and c of the question.