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?
數學統計題
2008-03-05 9:48 am
回答 (2)
2008-03-05 8:05 pm
✔ 最佳答案
(a) A diameter of 2.48 inches has a standard score of (2.48 - 2.50)/0.04 = -0.5So 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
參考: My Maths knowledge
2008-03-06 2:29 am
(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
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
參考: me friend
收錄日期: 2021-04-21 01:37:46
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