A sample of size 30 is taken from a population and the height of each person is recorded.

4.8 4.8 4.0 5.2 5.5 4.7 5.6 5.5 4.9 5.0 5.2 4.6 5.6 4.9 5.1 5.2 5.2 5.5 4.3
5.2 5.2 5.2 4.7 5.3 4.8 4.4 4.4 5.2 4.6 5.1

1. Construct a frequency distribution table with 6 classes.

2. Plot a histogram and explain the shape of the distribution

3. Compute the mean and standard deviation of the data, using the frequency distribution.

4. What percentage of the observations falls within 1 standard deviations of the sample mean?

5. What percentage of the observations falls within 2 standard deviations of the sample mean?

6. Are the result of parts d and e coinciding with the empirical rule?

11. A sample of 30 used cars sold by an auto dealership in 2009 revealed that the correlation between selling price and number of kilometres driven was −0.45. We want to test, at the 1% significance level, if there is a negative linear relationship in the population between selling price and number of kilometres driven. According to the p-value given in the table, our conclusion would be to reject the null hypothesis and conclude that the sample evidence supports the claim of a negative linear relationship at the 1% significance level.

True or False

15.

For any given number of hours studied, we expect actual grade to lie within about +/- 18.24% of the predicted mean grade ______% of the time. Do Not include the % sign. Use the Empirical rule (68-95-99.7) to answer this.

l. Find the standard deviation.

            m. Find the coefficient of variation.

            n. What is the 80^th percentile of this data set?

            o. Does this data set have any outliers? Use statistics in answering this question (not just your opinion).

            p. Would you use the Empirical rule or Chebyshev’s Theorem here and why?

            q. Based on the mean and median calculated above, would you expect this data to be symmetric, skewed to the left or skewed to the right and why?

Birth rates (births per 1000 population) for 30 randomly selected countries are given below: 44.6 39.1 46.5 20.6 15.5 12.1 41.5 12.1 36.2 30.6 12.9 47.3 33.8 47.3 39.8 42.2 14.5 21.4 19.4 16.9 27.7 17.2 14.1 11.2 33.5 13.5 34.7 37.4 36.7 45.5 a) Construct a relative frequency histogram for the data (use k = 5 intervals !!!), b) Construct a cumulative relative frequency histogram (an empirical distribution function), c) Using grouped data estimate the unknown population mean µ and the population variance. d) What is the estimate of probability that a random variable X that has generated those data, will take the value of 12.1? Explain.

At a Midwestern business school, historical data indicates that 70% of admitted MBA students ultimately join the business school’s MBA program. In a certain year, the MBA program at the University admitted 200 students.

a. Find the probability that at least 150 students ultimately join the MBA program.

b. Find the probability that no less than 135 and no more than 160 students finally join the MBA program.

c. How many students should the MBA program expect to join the program?

d. What is the standard deviation of the number of students who will join the MBA program? e. Let X be the number of students out of 200 who will join the program. Would the empirical rule apply to the probability distribution of X in this case?

Try to solve these problems using the Table method

3. Combustion analysis was performed on 1.50 g of a compound containing C, H and N to yield 3.21 g of carbon dioxide and 0.981 g of water. What is the empirical formula of this compound?

4. A 3.82-g sample of magnesium nitride is reacted with 7.73 g of water. Mg3N2 (s) + 3 H2O (ℓ) → 2 NH3 (g) + 3 MgO (s) The yield of MgO is 3.60 g. What is the percent yield in the reaction?

5. a) A beaker contains 200.0 mL of 0.250 M AgNO3. 200 mL of 0.100 M HCl(aq) is added to it. What is the NO3 − concentration in the final mixture?

b) What is the Ag+ concentration in the final mixture?

Please explain why

Until recently, many philosophers and psychologists thought that unconscious emotions are impossible. It was believed that the essence of an emotion is to be felt. However, if we are not aware of something it cannot be felt. Hence, it was concluded that we must be conscious of our emotions.

For this research project your job is to find empirical evidence supporting the existence of unconscious emotions. Your data should be distinct from anything you read in A General Theory of Love. You can find your data online, just be sure to cite your source. Once you have the data, explain why it supports the existence of unconscious emotions. In your write up, make sure to address the skeptic, that is, someone who believes there cannot be unconscious emotions.

Minimum length 500 words.

On January 1, 2018, the Highlands Company began construction on a new manufacturing facility for its own use. The building was completed in 2019. The company borrowed $1,550,000 at 7% on January 1 to help finance the construction. In addition to the construction loan, Highlands had the following debt outstanding throughout 2018: $9,000,000, 11% bonds $3,000,000, 7% long-term note Construction expenditures incurred during 2018 were as follows: January 1 $ 680,000 March 31 1,280,000 June 30 896,000 September 30 680,000 December 31 480,000 Required: Calculate the amount of interest capitalized for 2018 using the specific interest method. (Do not round the intermediate calculations. Round your percentage answers to 1 decimal place (i.e. 0.123 should be entered as 12.3%).)

The prepaid insurance account has an unadjusted balance of $46,000 at December 31,

2018, the end of Hanson Company's accounting year. Insurance expense has a $2,000 balance

at the same point in time.

The following policies are in effect at December 31, 2018:

Policy Type Date Acquired   Policy Term Total Premium Paid When Acquired

Liability 1-31-17 2 years $48,000

Auto 6-30-18 2 years . $9,000

Business interruption . 8-1-18 1 year $840

1. Determine the adjusted balance in prepaid insurance at December 31, 2018.

2. Determine the amount of total insurance expense (you need not separate the expense

by policy type) to report on the income statement for the year ended December 31,

2018.