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AP Statistics/Unit 5: Sampling Distributions
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Probability for Difference in Sample Means

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Two independent random samples, of sizes n1=36n_1 = 36 and n2=64n_2 = 64, are selected from two normally distributed populations. The first population has a mean of μ1=75μ_1 = 75 and a standard deviation of σ1=12σ_1 = 12. The second population has a mean of μ2=68μ_2 = 68 and a standard deviation of σ2=15σ_2 = 15. What is the probability that the difference between the sample means, (xˉ1−xˉ2\bar{x}_1 - \bar{x}_2), is greater than 10?

A

0.5000

B

0.1314

C

0.0228

D

0.9938

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