Question 1, 2, 3 is True OR False

1. If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and it is assumed that the amount of gasoline purchased per car when graphed is symmetrical, then there is approximately a 68.26% chance that a random sample of 9 cars will have a sample mean between 14 and 67 gallons.

a. True

b. False

2. The sampling distribution of the proportion approximately follows the normal distribution when np15 and n(1-p)15.

a. True

b. False

3. The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.

a. True

b. False

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Question 4 and 5 (show work)

4. Beyond financial compensation, what is important to employees? Many employees in the Department of Homeland Security rated the ability to telework. At least 74% of workers said that flexibility in terms telework is what they most desire. When a sample of 65 employees at DHS were asked, what is the probability that in the sample, more than 72% say telework is important?

5. The sale of non-alcoholic beer is sky-rocking. Most are low calorie and low carbs. The mean carbohydrate level per the top brands is 42.1 carbs per 16oz bottle with a standard deviation of 10 carbs. Assuming an approximate normal distribution, what is the probability that a top brand has between 10 and 20 carbs.