Standard normal distribution help in stats
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Standard normal distribution help in stats

[From: ] [author: ] [Date: 12-05-02] [Hit: ]
(a) If we take many samples, the sample mean [x] varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution?(b) According to the 68 part of the 68-95-99.7 rule, 68% of all values of [x] fall within _______ on either side of the unknown mean μ.......
The National Assessment of Educational Progress (NAEP) gave a test of basic arithmetic and the ability to apply it in everyday life to a sample of 840 men 21 to 25 years of age. Scores range from 0 to 500; for example, someone with a score of 325 can determine the price of a meal from a menu. The mean score for these 840 young men was [x] = 272. We want to estimate the mean score μ in the population of all young men. Consider the NAEP sample as an SRS from a Normal population with standard deviation σ = 60.

(a) If we take many samples, the sample mean [x] varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution?

(b) According to the 68 part of the 68-95-99.7 rule, 68% of all values of [x] fall within _______ on either side of the unknown mean μ. What is the missing number?

(c) What is the 68% confidence interval for the population mean score μ based on this one sample? Note: Use the 68-95-99.7 rule to find the interval.

-
a)
What is the standard deviation of this sampling distribution?
σ /√n
= 60/√840
=2.0702

b)
1 standard deviation of the mean
= (1) 2.07
= 2.07

c)
272+/- 1(2.07)
(269.93, 274.07)
1
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