1. The mean value of land and buildings per acre from a sample of farms is $1600

Question

1. The mean value of land and buildings per acre from a sample of farms is $1600, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 73. Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1500 and $1700. If 27 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1500 per acre and $1700 per acre?

2. 33% of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.

3. Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $63,500. A random sample of 32 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $61,000? Assume =$5,800.

4. The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 204 milligrams per deciliter and a standard deviation of 37.9 milligrams per deciliter. (a) What percent of the men have a total cholesterol level less than 229 milligrams per deciliter of blood? (b) If 249 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 263 milligrams per deciliter of blood?

5. A horse race has 11 entries and one person owns 2 of those horses. Assuming that there are no ties, what is the probability that those two horses finish first and second (regardless of order)?

6. Construct the confidence interval for the population mean . c=0.90, x=7.8, =0.9, and n=55 A 90% confidence interval for is

7. Use the value of the linear correlation coefficient to calculate the coefficient of determination. r= -0.951 Calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line? % of the variation is unexplained and is due to other factors or to sampling error?

8. A machine cuts plastic into sheets that are 45 feet (540 inches) long. Assume that the population of lengths is normally distributed. The company wants to estimate the mean length the machine is cutting the plastic within 0.25 inch. Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 0.50 inch? Repeat part (a) using an error tolerance of 0.125 inch?

9. In a sample of 1100 U.S. adults, 213 dine out at a restaurant more than once per week. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults (a) Find the probability that both adults dine out more than once per week. (b) Find the probability that neither adult dines out more than once per week. (c) Find the probability that at least one of the two adults dines out more than once per week.

10. Assume the Poisson distribution applies. Use the given mean to find the indicated probability. Find P(6) when =8.

Explanation / Answer

As multiple questions are posted, only the first one will be answered,

1. Mean = 1600

Standard deviation = 100

According to empirical rule, 68% of data in a bell shaped distribution lies with 1 standard deviation of the mean.

Or, P(1600-100 < X < 1600+100) = 68%

or, P(1500 < X < 1700) = 68%

Thus, the number of farms whose land and building values per acre are between $1500 and $1700 = 73*68%

= 49.64 or 50 (rounded off)

Expected number of additional farms whose land and building values per acre are between $1500 and $1700

= 27*68%

= 18.36 or 18 (rounded off)

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