Statistics Question 9.30

If you draw an M&M candy at random from a bag of the candies, the candy you draw will have on of seven colors. The probability of drawing each color depends on the proportion of each color among all candies made. Here is the distribution for milk chocolate M&M’s

1. What must be the probability of drawing a blue candy?
2. What is the probability that you do not draw a brown candy?
3. What is the probability that the candy you draw is yellow, orange, or red?

Statistics Question 10.20

In March 2000 the bureau of Labor Statistics recorded the incomes of 55,899 people as a population people between the ages of 25 and 65 who had worked but whose main work was not in agriculture. We will treat these 55,899 people as a population. As is usually the case, the distribution of incomes in this population is strongly skewed to the right. To estimate the mean income in this population, we can select an SRS and use the sample mean (x) to estimate the unknown population mean. How will the sample mean behave when we take many samples?

We used software to choose 1000SRSs of size 25 and another 1000 SRSs of size 100. Figure 10.9 shows histograms of the two sets of 1000 sample means, using the same classes and drawn to the same scale for easy comparison.

1. Which distribution is closer in shape to the bell curve of a Normal distribution? What important fact about sampling distributions does this comparison illustrate?
2. About what is the range (from smallest to largest) of the sample means for samples of size 25? For samples of size 100? What important fact about sampling distributions does this comparison illustrate?
3. Based on the sample means for samples of size 100, about what is the value of the mean income for this entire population?

Statistics Question 10.22

A laboratory weighs filters from a coal mine to measure the amount of dust in the mine atmosphere. Repeated measurements of the weight of dust on the same filter vary normally with standard deviation = 0.08 milligram (mg) because the weighing is not perfectly precise. The dust on a particular filter actually weight 123 mg. Repeated weighing will then have the Normal distribution with the mean 123 mg and standard deviation 0.08 mg.

1. The laboratory reports the mean of 3 weighing. What is the distribution of this mean?
2. What is the probability that the laboratory reports a weight of 124 mg or higher for this filter?

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