AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Combining Two Random VariablesQuestion 3
3
QuizMultiple Choice

Combining Two Random Variables

Question 3 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S – T.What is the probability that Soledad sends more texts on a randomly selected day?

Answer
A
0.104
B
0.214
C
0.786
D
0.896

Explanation

Because S and T are independent, the difference D = S − T is Normally distributed with mean 100 − 108 = −8 and standard deviation √(6² + 8.1²) ≈ 10.08. Soledad sends more texts when D > 0, which has probability P(Z > (0 − (−8))/10.08) = P(Z > 0.79) ≈ 0.214. The correct choice is 0.214.

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