Let X1 be a normal random variable with mean 134 and variance 64. Let X2 be a normal random variable with mean 147 and variance 81. Suppose we take independent random samples of 25 items from population 1 and 25 items from population 2. Find the following: ¯ ¯ (a) P( X1− X2 ≤ −7) ¯ ¯ (b) P( X1− X2 >8) (c) P(−11 ≤¯ X1− ¯ X2 ≤ 2)

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07-07-2024
Mathematics

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Let X1 be a normal random variable with mean 134 and variance 64. Let X2 be a normal random variable with mean 147 and variance 81. Suppose we take independent random samples of 25 items from population 1 and 25 items from population 2. Find the following: ¯ ¯ (a) P( X1− X2 ≤ −7) ¯ ¯ (b) P( X1− X2 >8) (c) P(−11 ≤¯ X1− ¯ X2 ≤ 2)

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