# Central Theorem, population shape, Tootsie Roll samples

5. State the main points of the Central Limit Theorem for a mean.

6. Why is population shape of concern when estimating a mean? What does sample size have to do with it?

8.46-A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on

a very accurate scale. The results in grams were

3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

(a) Construct a 90 percent confidence interval for the true mean weight.

(b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?

(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during

manufacture. (Data are from a project by MBA student Henry Scussel.)

8.62 In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.

(b) Why is the normality assumption not a problem, despite the very small value of p? (Data are from Flying 120, no. 11 [November 1993], p. 31.)

https://brainmass.com/business/strategy-and-business-analysis/central-theorem-population-shape-tootsie-roll-samples-faa-drug-testing-207067

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5. State the main points of the Central Limit Theorem for a mean.

Central Limit Theorem

The Central Limit Theorem shows the accuracy of the approximation larger improves as N ". The Central Limit Theorem predicts that regardless of the distribution of the "Parent population":

[1] The mean of the population of means is always equal to the mean of the parent population from which the population samples were drawn.

[2] The standard deviation of the population of means is always equal to the standard deviation of the parent population divided by the square root of the sample size (N).

[3] The distribution of means will increasingly approximate a normal distribution as the size N of samples ...

#### Solution Summary

Central theorem and population shape for Tootsie Roll samples are analyzed.