AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Combining Two Random VariablesQuestion 9
9
QuizMultiple Choice

Combining Two Random Variables

Question 9 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

The weight of panda bears, P, is approximately Normally distributed with a mean of 185 pounds and a standard deviation of 12.3 pounds. The weight of koala bears, K, is approximately Normally distributed with a mean of 21.5 pounds and a standard deviation of 4.8 pounds. Suppose a zookeeper randomly chooses a panda and a koala bear, where P and K are independent random variables.What is the probability that the total weight for the two animals is 225 pounds or more?

Answer
A
0.020
B
0.081
C
0.195
D
0.851

Explanation

Because the weights are independent, the total weight has mean 185 + 21.5 = 206.5 pounds and standard deviation √(12.3² + 4.8²) ≈ 13.2 pounds. A total of 225 pounds is about (225 − 206.5)/13.2 ≈ 1.40 standard deviations above the mean. The probability of being at least 1.40 standard deviations above the mean is about 0.081, so the answer is 0.081.

AI-written and checked against the verified answer.

Previous
Next

More from this Course

Quiz
10 verified answers

Choosing the Appropriate Inference Procedure

Quiz
10 verified answers

Conditional Probabilities

Quiz
10 verified answers

Estimating the Mean Difference