MA 214 Probability and Statistics for Business
Dr. Ed Donley
Test 1
October 1, 1997

  1. (8 points) Classify the following examples of data as nominal, ordinal, interval, or ratio.

    1. The number of years of service of all employees of a certain factory

      ratio

    2. The species of trees grown on a tree farm.

      nominal

    3. The time required to assemble a carburator.

      ratio

    4. The class (freshman, sophmore, junior, senior) of students in a statistics class.

      ordinal

  2. (11 points) In a survey of 200 companies, 120 contracted for outside pension plans for their employees, 50 had their own pension funds, and 30 had a combination plan. Construct a relative frequency bar chart for these pension plans.

    Relative Frequencies
    Outside120/200 = .60
    Own50/200 = .25
    Combined30/200 = .15

  3. (7 points) IQ scores have a mean of 100 and standard deviation 16. Find the z-score for an IQ of 130. The distribution of IQ scores is mound-shaped. Is an IQ of 130 unusual? Why?

    z = (x - m)/s = (130 - 100)/16 = 1.875

    This is fairly high IQ, but it is not rare, since 95% of IQs have z-scores between -2 and 2.

  4. (20 points) The ages of a sample of 6 students are:

    20, 18, 18, 21, 20, 18.

    Compute the following.

    1. mean

      = (20 + 18 + 18 + 21 + 20 + 18)/6 = 115/6 = 19.17

    2. median

      Rank the data:
      18, 18, 18, 20, 20, 21

      median = (18 + 20)/2 = 19

    3. mode

      Most frequent value is 18

    4. range

      Largest minus smallest is 21 - 18 = 3

    5. first quartile

      i = p/n x 100 = 25/6 x 100 = 1.5

      Round up to 2. First quartile is x2 = 18

    6. third quartile

      i = p/n x 100 = 75/6 x 100 = 4.5

      Round up to 5. First quartile is x5 = 20

    7. interquartile range

      Q3 - Q1 = 20 - 18 = 2

    8. variance

      s2 = [ (20 - 19.17)2 + (18 - 19.17)2 + (18 - 19.17)2 + (21 - 19.17)2 + (20 - 19.17)2 + (18 - 19.17)2 ]/5 = [0.6889 + 1.3689 + 1.3689 + 3.3489 + 0.6889+ 1.3689]/5 = 8.8534/5 = 1.77

    9. standard deviation

  5. (10 points) Suppose that the duration of long-distance telephone calls from at a company has mean 12 minutes and standard deviation 3 minutes. At least what portion of the calls are between 8 minutes and 16 minutes long?

    Use the empirical rule. The z-scores for 8 and 16 are z = (8 - 12)/3 = -4/3 and z = (16-12)/3 = 4/3. So, k = 4/3 in the empirical rule. At least 1 - 1/k2 = 1 - 1/(4/3)2 = 7/16 = 0.4375 of the data is within k = 4/3 standard deviations of the mean.

  6. (8 points) A sample of 20 states are classified according to the majority party in their state legislatures and their state sales tax rates. Find the probability that a predominantly democratic state has a low sales tax rate.
    DemocraticRepublican
    High taxes54
    Low taxes47

    P(low tax | democratic) = 4/(5 + 4) = 4/9 = 0.44

  7. (9 points) Forty percent of the residents of a community read the grocery advertisements in the local newspaper. There is a 30% chance that someone who reads an ad for a bakery sale will buy something from the bakery. What is the probability that a randomly chosen resident of the community will see the ad and buy from the bakery?

    S . . . See the ad

    B . . . Buy from the bakery

    P(S) = 0.40

    P(B | S) = 0.30

    Find P(S and B) = P(S B) = P(B | S) P(S) = 0.30 x 0.40 = 0.12

  8. (15 points) An oil company is drilling test wells in Alaska and Texas. The managers of the company feel that the chance of finding oil in Texas is 0.6 and the chance of finding oil in Alaska is 0.8.

    1. Find the probability that exactly one of the two wells finds oil.

      P(exactly one) = P(Texas and not Alaska or Alaska and not Texas)

      = P(Texas) P(not Alaska) + P(Alaska) P(not Texas)

      = (0.6)(0.2) + (0.8)(0.4) = 0.12 + 0.32 = 0.44

    2. Find the probability that neither well finds oil.

      P(neither) = P(not Texas and not Alaska) = P(not Texas) P(not Alaska) = (0.4)(0.2) = 0.08

  9. (7 points) How many ways can you select a 5-card hand from a 52-card deck?