APFIVE Probability for Difference in Sample Means
Independent random samples are drawn from two normally distributed populations. Population 1 has $$μ_1 = 75$$ and $$σ_1 = 12$$. Population 2 has $$μ_2 = 68$$ and $$σ_2 = 15$$. If $$n_1 = 36$$ and $$n_2 = 64$$, what is the probability that the difference in sample means ($$\bar{x}_1 - \bar{x}_2$$) is greater than 10?
A
0.5000
B
0.9938
C
0.0228
D
0.1314
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