Merced College; Don Power

 

Math 10 - Study Guide, Chapters  6, 7, 8

 

1.  Can the given values be looked on as the values of a probability distribution of a random variable which can take on the values 1, 2, 3, or 4?  Why or why not?

f(1) = ____, f(2) = ______, f(3) = _____, f(4) = _____

 

2.  According to the Department of Defense, ____ % of all Air Force recruits have graduated from high school.  If ____ Air Force recruits are selected at random, find the probability that exactly ___ of them have graduated from high school.  You should be able to use the table supplied with our book (to save time), or use a formula for this calculation (if the table will not work).

 

3.  In a given city, medical expenses are given as the reason for ____% of all personal bankruptcies. 
What is the probability that, of the next ____ bankruptcies, less than ____ will be due to medical expenses?

 

4.  Among the ____ applicants for a job, ___ have college degrees.  If __ applicants are chosen at random, what is the probability that exactly __ of them have college degrees?  What type of distribution is this?  Would it be legitimate to approximate it with a normal distribution?  Why or why not?

 

5.  If experience has shown that an average of ___ students visit the Math Lab from 1:00 to 2:00 on Wednesdays, what is the probability that exactly ___ students will visit the Math Lab during that time frame on a given Wednesday?

 

6.  Four cards are drawn at random from a deck of unknown composition.  The probabilities of drawing
      0, 1, 2, 3, or 4 red cards are found to be

 

Number of red cards

0

1

2

3

4

 

Probability

____

____

____

____

____

Find the mean and standard deviation of this probability distribution.

 

7.  In a quality control study, it was found that ___% of all auto frames manufactured by one company had at least one defective weld.  If the frames are examined in groups of ___, find the mean and standard deviation of the number of frames with defective welds.

 

8.  The annual number of rainy days in a certain city is a random variable with m = ____ and s = ____.  According to Chebyshev’s theorem, with what probability can we assert that it will rain in that city between ____ and ____ days?

 

9.  Find the area under the standard normal curve which lies between z = _____and z = _____

 

10.  Find z if the normal-curve area to the left of z is ____.   [or to the right of z....]

 

11.  A random variable has a normal distribution with m = _____ and s = ____   What is the probability that this random variable will take on a value between ____ and ____?

 

12.  A normal distribution has a mean m = _____.  Find the standard deviation if ____% of the area under the curve lies to the right of _____.

 

13.  A salesman who drives from Fresno to Modesto finds that his driving time is a random variable having a normal distribution with m = ____ minutes and s = ___ minutes.  Find the probability that such a trip will take less than _____ minutes.

 

14.  a.  A restaurant manager knows from experience that the number of customers at lunchtime can be approximated by a normal distribution with m = _____ customers and s = _____ customers.  Use the normal distribution to find the probability that the restaurant will have exactly ___ customers.

 

      b. Is the probability in part a really binomial, hypergeometric, or Poisson?  Calculate the probability using the appropriate procedure, and determine the error that resulted from using the normal distribution in part a.

 

15.  An airline experiences a ___% rate of no-shows on advance reservations [between 6% and 8%]

a.  Assuming there are over 100 seats per airplane, explain why it is valid to use the normal distribution for this calculation.

b.  Find the probability that of ______ randomly selected advance reservations, there will be at least _____ no-shows.

 

16.  A researcher needs to select ___ dairy cows at random from a herd of ___ cows with ear tags numbered from 1 to ____.  Make the selection using columns ___ and ___ of the random number table provided with the test, beginning at the top of the page.

 

17.  Calculate the standard error of the mean  () in the case where samples of size ___ are selected from a population of  _____ individuals with a mean of m = ___ and a standard deviation of  s = ___.

 

18.  The ages of U.S. commercial aircraft have a mean of ____ years and a standard deviation of  ___ years.  If the Federal Aviation Administration randomly selects ___ commercial aircraft for stress tests, find the probability that the mean age of the sample group is greater than ____ years.

 

19.  A medical researcher wants to estimate the mean systolic blood pressures of women between the ages of 18 and 24.  She conducts a survey of ____ women and finds that their blood pressures (in mm Hg) have a mean of   = _____ and a standard deviation of  s = ____  If she assumes that the standard deviation of the population as a whole is also ____, what will be the probability that her sample mean will be in error by less than  ____ mm Hg?

 

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