Question

Road Runner (of Looney Tunes fame) is deciding on its new adventure. When not outrunning everyone, Road Runner has a passion for statistics and has calculated that the estimated number of interactions it has with Wile E. Coyote each year is 63, with a variance of 150. This year, Road Runner only met Wile E. Coyote 50 times. So, Road Runner is wondering how many run-ins to anticipate next year. What is the probability that Road Runner meets Wile E. Coyote more than 70 times next year? Select the answer that has the probability within its range.

a. 0% to 15%

b. 15% to 30%

c. 30% to 45%

d. 45% to 60%

Answer 1

The probability that Road Runner meets Wile E. Coyote more than 70 times next year is about 28.43%, falling within the range of 15% to 30%.

Step-by-step explanation:

To calculate the probability that Road Runner meets Wile E. Coyote more than 70 times next year, given an estimated number of interactions is 63 with a variance of 150, we can assume the number of interactions follows a normal distribution due to the Central Limit Theorem.

First, we find the standard deviation by taking the square root of the variance, which is √150. This gives us a standard deviation of approximately 12.25. We are looking for P(X > 70), where X is the number of interactions next year. To find this probability, we use the Z-score formula:

Z = (X - μ) / σ

For X = 70, μ = 63 and σ = 12.25:

Z = (70 - 63) / 12.25 ≈ 0.57

Consulting a standard normal distribution table or using a calculator, we find the probability corresponding to Z = 0.57 and subtract from 1 since we want the area to the right of this Z-score:

P(Z > 0.57) = 1 - P(Z < 0.57) ≈ 1 - 0.7157 = 0.2843

Hence, the probability that Road Runner meets Wile E. Coyote more than 70 times next year is approximately 28.43%, which is within the range of 15% to 30%.