Question

Solaris is a firm that can install solar panels at an airport to generate electricity for the airport’s usage. The company claims that in 70 percent of all airports where its solar panels are installed, an airport’s electricity bill is reduced by at least 40 percent. The probability that an airport’s electricity bill is reduced by at least 40 percent, in seven out of ten airports where the company’s solar panels are installed, equals approximately:

• A. 0.082
• B. 0.002
• C. 0.490
• D. 0.267

Hint:

For binomial distribution problems, use the binomial probability formula and calculate the sum for the required range of successes.

Answer 1

The Correct Option is D

Step 1: Understand the problem

This is a binomial probability problem where the success probability (reduction in the electricity bill) is 70% (or 0.7) for each airport. We are interested in the probability that at least 7 out of 10 airports will achieve this reduction.

Step 2: Use the binomial probability formula

The probability of getting exactly \( k \) successes in \( n \) trials is given by the binomial distribution formula:

\[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \]

Where:

• n = 10 (the number of trials or airports),
• p = 0.7 (the probability of success),
• k = 7 (the number of successes we are interested in).

Using the formula, we can calculate the probability that the electricity bill is reduced in at least 7 out of 10 airports. The answer is approximately 0.267.