Chapter 5

 

  1. Offspring of a particular genetic cross have an undesirable trait

     with probability 1/8. Inheritance of this trait by separate

     offspring is independent. You examine 100 offspring from this cross

     and count the number X who have the undesirable trait.

       a.) What is the mean of X?

       b.) What is the probability that the number of offspring having

           this trait is at least 10 but not more than 15?

 

  2. Offspring of a particular genetic cross have an undesirable trait

     with probability 1/8. Inheritance of this trait by separate

     offspring is independent. You examine 200 offspring from this cross

     and count the number X who have the undesirable trait. What is the

     standard deviation of X?

 

  3. Suppose that the proportion of a toxic chemical in waste water

     output from a mill varies over time according to a normal

     distribution with mean 0.005 and standard deviation 0.0012. An

     environmental group takes samples on 9 dates and uses the sample

     mean  in a report on local environmental problems. Find

                     P[0.004 <  < 0.006]

     which is the probability that their estimate is correct within

      0.001.

 

  4. Suppose that the proportion of a toxic chemical in waste water

     output from a mill varies over time according to a normal

     distribution with mean 0.005 and standard deviation 0.0012. Samples

     on 9 dates are taken and the sample mean  is reported. If the

     sample mean is .005 or above, the mill will be required to pay a

     large fine. What is the probability that they will have to pay the

     fine?

 

  5. About 9% of the residents of Indiana are black.  You choose Indiana

     residents at random (independently of each other) for an opinion

     poll. You choose 450 people in all.  What is the mean number of

     blacks among the people chosen?

 

  6. The yield of irrigated corn under standard conditions of culture in

     plots on a Nebraska experimental farm is normally distributed with

      = 120 and  = 6 bushels per acre. How many plots must a researcher

     plant if he wants the sample mean yield  to have a standard            

     deviation  = 2 bu/acre?

  7. The yield of irrigated corn under standard conditions of culture in

     plots on a Nebraska experimental farm is normally distributed with

      = 120 and  = 6 bushels per acre. If the researcher plants 9                                                     

     plots, what is the probability that the mean yield  is greater than

     125 bushels per acre?

 

  8. In a study of plant safety, it was found that the time it took for

     machine operators to react to a warning light was normally

     distributed with mean 1 second and standard deviation 0.3 second.

     What is the probability that an individual operator will not react

     within 1.5 seconds?

 

 9. University X conducts a sample survey of families of undergraduate

     students to obtain their opinions about health insurance for

     students.  A questionnaire is sent to a simple random sample of 100

     families.  One question  asks for a response to the statement

     "University X should provide full medical insurance for students

     even if tuition must be raised to pay for it."   The possible

     responses are (1) Strongly agree, (2) Agree, (3) Neutral, (4)

     Disagree, and (5) Strongly disagree. The random variable X records

     which answer a family gives to the question.  So the possible values

     of X are  1, 2, 3, 4, and 5. X is

     (a) a discrete random variable that is not binomial

     (b) a discrete random variable that is binomial

     (c) a continuous random variable that is not normal

     (d) a continuous random variable that is normal

 

 10. The annual rate of return on common stocks (as measured by the

     Standard & Poor's 500-stock index) varies from year to year

     according to a normal distribution with mean 12% and standard

     deviation 20%.  A rate of return less than zero means that investors

     lost money. What is the probability that the rate of return is less

     than 0 in any single year?

 

 11. British government data classify people into five occupational

     classes, from Class 1 (professional and managerial) down to Class 5

     (unskilled labor).  Below is the probability distribution for the

     class of a randomly drawn male of Indian ancestry. (Based on British

     labor force surveys, reported in the Economist, October 28, 1989.)

    

          Class           1     2     3    3b    4     5

          Probability   0.14  0.15  0.17  0.35  0.16  0.03

    

     Let the random variable X be the class of a randomly chosen Indian

     man.  Is X continuous or discrete?  Does X have a binomial

     distribution?