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數學統計題

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1.The diameter of tennis balls manufactured at a large factory is approximately normally distributed with a mean of 2.50 inches and a standard deviation of 0.04 inch.(a)What is the probability that a randomly selected tennis ball will have a diameter less than 2.48 inches?If many random samples of 16 tennis... 顯示更多 1.The diameter of tennis balls manufactured at a large factory is approximately normally distributed with a mean of 2.50 inches and a standard deviation of 0.04 inch. (a)What is the probability that a randomly selected tennis ball will have a diameter less than 2.48 inches? If many random samples of 16 tennis balls are selected, (b)What will be the mean of the sample means and the standard error of the mean? (c)What distribution will the sample means follow? (d)What proportion of the sample means will be less than 2.48 inches?

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(a) A diameter of 2.48 inches has a standard score of (2.48 - 2.50)/0.04 = -0.5 So with z = 0.5, σ(z) = 0.1915 Therefore the probability that a randomly selected ball will have a diameter less than 2.48 inches is 0.5 - 0.1915 = 0.3085 (b) The mean of the sample means will still be 2.50 inches with standard error equal to: At 5% of significance level: 1.96σ/√n = 1.96 x 0.04/√16 = 0.0196 inches (c) Normal distribution (d) For a sample mean of 2.48 inches, its standard score is (2.48 - 2.50)/0.0196 = -1.02 So with z = 1.02, σ(z) = 0.3461 Therefore the proportion of sample means that will have be less than 2.48 inches is 0.5 - 0.3461 = 0.1539

其他解答:

(a) A diameter of 2.48 inches has a standard score of (2.48 - 2.50)/0.04 = -0.5 So with z = 0.5, σ(z) = 0.1915 Therefore the probability that a randomly selected ball will have a diameter less than 2.48 inches is 0.5 - 0.1915 = 0.3085 (b) The mean of the sample means will still be 2.50 inches with standard error equal to: At 5% of significance level: 1.96σ/√n = 1.96 x 0.04/√16 = 0.0196 inches (c) Normal distribution (d) For a sample mean of 2.48 inches, its standard score is (2.48 - 2.50)/0.0196 = -1.02 So with z = 1.02, σ(z) = 0.3461 Therefore the proportion of sample means that will have be less than 2.48 inches is 0.5 - 0.3461 = 0.1539