Download Finite Mathematics Test 5

Finite Mathematics
Test 5
Name (please print)_______________________________________________
1. Let A and B be two events and p(A) = .6, p(B) = .7, p(A/B) = .5.
Find p( A  B), p( A  B), p( B / A) .
2. Seven cards are taken at random from a standard deck of 52 cards. What is
the probability to have at least two cards of the same kind?
3. A high school graduate applies to five colleges and estimates his chances to be
admitted as respectively 0.3, 0.5, 0.5, 0.7, and 0.8. What is the probability that he
will be admitted to at least one of these colleges?
4. A box contains 5 quarters, 6 nickels, and 8 dimes. Three times a coin is taken at
random and returned to the box. What is the probability to have at least two coins
of different denomination?
5. The same question as in Problem 4 but the coins are not returned into the box.
6. In the conditions of problem 5 what is the probability to have coins of three
different denominations if the first coin is a dime?
7. Two fair dice are rolled 10 times. What is the probability to have the sum of the
top numbers equal to 7 exactly 4 times?
8. Find the area under the standard normal curve over the interval –1.56 < z < .79.
9. For a large group of people the upper level of blood pressure is measured. The
mean of the measurements is 115 and the standard deviation is 10. Assume the
normal distribution of the measurements and find the percentage of people with
the upper level of blood pressure between 100 and 140.
10. The results of rolling a die 15 times are 1, 6, 1, 4, 5, 3, 2, 3, 1, 5, 6, 4, 2, 3, 3.
(a) Find the frequencies and the relative frequencies.
Item
Frequency
Relative Frequency
(b) Find the sample mean m and the sample standard deviation s.
(c) Find the median and the mode.
(d) Construct a histogram.
11. A fair die is rolled 6000 times. Find the probability that the number of 6’s on
the top face will be between 990 and 1015.
12. For the paired data values
x
1
y
9
4
7
6
8
1. Find the equation of the regression line.
2. Plot the data and the regression line.
3. Use your equation to predict the value of y when x = 3.
4. Find the correlation coefficient r.
7
1