2
QuizMultiple Choice

Unit Test — Unit test

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

Renee and Thomas live at the beach and collect seashells. The number of shells Renee collects on any given day, R, is approximately Normal with a mean of 58.2 shells and a standard deviation of 12.8 shells. The number of shells Thomas collects on any given day, T, is approximately Normal with a mean of 47.9 shells and a standard deviation of 11.5 shells. Assume the two random variables are independent of each other.What is the probability that on a randomly selected day the total number of shells collected by Renee and Thomas is 120 or more?

Answer
A
0.002
B
0.209
C
0.284
D
0.791

Explanation

Because Renee’s and Thomas’s shell counts are independent, their total is approximately Normal with mean 58.2 + 47.9 = 106.1 and standard deviation √(12.8² + 11.5²) ≈ 17.2. For 120 shells, the z-score is (120 − 106.1) ÷ 17.2 ≈ 0.81. The probability of a total of 120 or more is the upper-tail probability, about 0.209, so the answer is 0.209.

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