m sample of size n₁ = 13 is selected from a normal population with a mean of 76 and a standard deviation of 7. A second sample of size n₂ = 9 is taken from another normal population with mean 68 and standard deviation 15. Let X₁ and X₂ be the ple means. Find: probability that X₁ X₂ exceeds 3. probability that 4.1 ≤ X₁ X₂ 5.4. your answers to two decimal places (e.g. 98.76).

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A random sample of size n₁ = 13 is selected from a normal population with a mean of 76 and a standard deviation of 7. A second
random sample of size n₂ = 9 is taken from another normal population with mean 68 and standard deviation 15. Let X₁ and X₂ be the
two sample means. Find:
(a) The probability that X₁
X₂ exceeds 3.
(b) The probability that 4.1
X₁ X₂ ≤ 5.4.
Round your answers to two decimal places (e.g. 98.76).
(a)
(b)
Transcribed Image Text:A random sample of size n₁ = 13 is selected from a normal population with a mean of 76 and a standard deviation of 7. A second random sample of size n₂ = 9 is taken from another normal population with mean 68 and standard deviation 15. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ X₂ exceeds 3. (b) The probability that 4.1 X₁ X₂ ≤ 5.4. Round your answers to two decimal places (e.g. 98.76). (a) (b)
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