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?
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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