MTH 362 FALL 2001

 

Sample problems for Test 1

 

1.  Consider the following data   22 35 43 36 38 38 27 29 38 22.

Produce a stem-and-leaf plot of this data.  Use class intervals [20, 24], [25, 29],  [30, 34], [35, 39], [40,45].

Produce a relative frequency histogram.

2.      Calculate the mean, the median, the variance and the standard deviation of the data  given in the previous question.

3.                  Define the following terms: Experiment, outcome, sample space, event.

4.                  Two boxes contain each four balls  numbered 1, 2, 3, 4.  One ball is drawn from each box.

(a)    Write down the sample space of the experiment.

(b)    What is the probability of the event E: Both balls bear the same number?

5.                  Suppose A and B are two events such that P(A) = 0.25, P(B) = 0.5, P(AÇB) = 0.05.  What are the numerical values of

(a) P(AÈB)

(b) P(Ac)

(c) P(Ac ÈBc)

6.                  A box contains 4 right handed screws and 6 left handed screws.  One screw is taken out at random and put aside, and then another is taken out.  What is the probability of getting

(a) Two right handed screws?

(b)  A  left handed screw and a right handed screw?

 7.      A box contains 4 right handed screws and 6 left handed screws.  One screw is taken out of the box and put back in the box, and then a screw is taken out again. What is the probability of getting

(a)    Two right handed screws?

(b)     A  left handed screw and a right handed screw?

8.      How many license plates can one obtain

a.       with 5 letters, if repetitions are allowed.

b.                               with 5 letters, if there is no repetition allowed.

c.                                with 3 letters and 2 digits with no repetitions.

9.      How many committees of 4 members can be formed from a group of 15 people

(a)    if there is no distinction between the roles of the committee members,

(b)   if the committee consists of a president, a secretary and controller.

10.  Let X be the random variable measuring the thickness (in millimeters) of washers a machine turns out.  Assume that X has the density  f( x ) = kx if  0.9< x < 1.2, and 0 otherwise.  Find k.  What is the probability that a washer will have thickness between 0.95 and 1.05?

11.  A small filling station is supplied with gasoline every Saturday afternoon.  Assume that its volume X of sales in ten thousands of gallons has the density function f( x ) = 6x(1-x) if  0<x<1, and 0 otherwise.  Determine the variance, and the standardized variable.

 

 

GOOD LUCK!