Diablo Valley College

Business Administration Department

Business 240--Statistics

Exam #1: max = 150 points

Take home

  1. Each of the following two histograms represents the distribution of acceptance rates (percent accepted) among 25 business schools in 1995. The histograms use different class intervals, but are based on the same data. In each class interval, the left endpoint is included but not the right.
a) / [10 points] What percent of the 25 schools have an acceptance rate of less than 20%? Explain how you arrived at your answer.= 4/25 = 16%
b) / [10 points] Find “the middle” of the acceptance rates and “the range” or spread of the acceptance rates in each of the graphs above. Explain why they should be approximately the same for both histograms.Center = 30, Spread= range of ~45%, from 7.5% to 52.5%. They should be similar center and spread measures because the data in both histograms is the same.
  1. For a Business Ethics course containing 10 students, the maximum point total for the quarter was 200. The point totals for the 10 students are given in the stemplot below.

[10 points] Recreate the data for the stem plot to the left:

{116_,_118_,_121_,_124_,_128_,_133_,_137_,_142_,_146_,_179_}

  1. [10 points] Consumers’ Union measured the gas mileage in miles per gallon of 38 1978–1979 model automobiles on a special test track. The pie chart below provides information about the country of manufacture of the model cars used by Consumers’ Union.

Briefly describe the distribution of car models used by Consumer’s Union in their survey of fuel efficiency (no more than 25 words). Then, sketch a Pareto Chart of the same data in the square below:

The cars used by Consumer’s Union were primarily U.S. made (more than 50%). Japanese and German cars were also among the most tested for gas mileage (combine to ~25 to 30 percent). Swedish, Italian and French cars were also used in smaller proportions in their study.

  1. [20 points] Describe the time series plot below, which gives the share price in dollars of General Electric stock, and with the bar chart giving the volume in millions of shares exchanged. The plots are for the one-year period September 2001–September 2002. (Identify the trend, average price, spread in transaction prices, and, if relevant, the nature of the series—e.g., cyclical.)

  1. In two sections of a class of with 50 students each, the grades on an Accounting test are summarized in the following table:
  1. [10 points] Describe the center, spread and shape of the exam scores in the two sections included on the left.

Typical Scores were in the mid 80s and low 90s, give or take 12 points in both cases.

  1. [10 points] Which section performed better on average? B b/c 90 > 84
  2. [10 points] Compute the two coefficients of variation. In which section is more scattered in either absolute or relative value? Explain.12/84 = 1/7 = CVa > 12/90 = 2/15 = CVb. Section A’s scores are more scattered.
  3. [10 points] In which section is it more likely the case to find students who earned very low test scores, A? or B? Explain.In A b/c it is skewed to the left (mean < median) and the average score is lower. B has scores that are skewed right.
  1. [10 points] The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 2.5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? Explain your answer (hint: you may use the 68-95-99.7 rule or table A to provide the answer, definitely sketch a bell curve and show your answer graphically)

Lowest mark that passes = 62 – 2*11 = 62-22 = 40

  1. [10 points] The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?Explain your answer (hint: you should use MS Excel or table A to provide the answer, definitely sketch a bell curve and show your answer graphically. If you use excel to obtain your answer write out the formula syntax you employed to get your answer).

80% has a Z = 0.84, so X = 70 + 0.84*10 = 78.4 minutes

  1. [20 points] Birth weights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. Calculate the proportion of infants with birth weights between 125 oz. and 140 oz. (hint: you should use MS Excel or table A to provide the answer, definitely sketch a bell curve and show your answer graphically. If you use excel to obtain your answer write out the formula syntax you employed to get your answer).

P(125 < X < 140) = P(1 < Z < 2) = .9772 - .8413 = .1349

  1. [10 points] Draw a graph sketching the scatter plot of two variables that you are attempting to associate such that one variable (X) is skewed left, the other (Y) is skewed right, and the relationship between the two variables is summarized by the correlation value r = +0.80 (strong and direct association between X and Y). Draw an X and Y axis coordinate with a crosshair at the means for X and Y. be sure to have the trend line cut through the cross hair with an upward slope, and with dots close to the trendline so that 80 of dots line up in quadrant II and III (upward slope)