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1. Two fair cubes are rolled. The random variable X represents the difference between the values of the two cubes.
a) Find the mean of this probability distribution. (i.e. Find E[X] )
b) Find the variance and standard deviation of this probability distribution.
(i.e. Find V[X] and SD[X])
The random variables A and B are defined as follows:
A = X-10 and B = [(1/2)X]-5
c) Show that E[A] and E[B].
d) Find V[A] and V[B].
e) Arnold and Brian play a game using two fair cubes. The cubes are rolled, and Arnold records his score using the random variable A and Brian uses the random variable B. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.
Given that z is a standard normal random variable, compute the following
probabilities.
a) P (Z < 0.49)
b) P (0.52 < Z)
c) P (- 1.98 ≤ Z ≤ .49)
d) P (.52 ≤ Z ≤ 1.22)
e) P (- 1.75 ≤ Z ≤ - 1.04)
For the most recent year available, the mean annual cost to attend a private
university in the United States was $26,889. Assume the distribution of annual costs follows the
normal probability distribution and the standard deviation is $4,500. Ninety-five percent of all
students at private universities pay less than what amount?
Assume that the mean hourly cost to operate a commercial airplane
follows the normal distribution with a mean of $2,100 per hour and a standard deviation of $250.
What is the operating cost for the lowest 3 percent of the airplanes?
Given that Z is a standard normal random variable, find Z for each
situation.
a) The area between -Z and Z is .9030.
b) The area between -Z and Z is .9528.
As part of its quality assurance program, the Autolite Battery Company
conducts tests on battery life. For a particular D-cell alkaline battery, the mean life is 19 hours.
There are four newly hired salespersons at Honda Cars Taguig Branch. The
number of motorcycles
and9.sold by each newly hired salesperson last month was 4,5, 8,Complete the information needed in the table below.
a. How many samples of size 2 are possible?
b. List all possible samples of size 2.
Observation Sample
random samples of size n=2 are drawn from a finite population consisting of the numbers 5,6,7,8,9. compute fot the mean, variance and standard deviation of the population, and the mean, variance and standard deviation of the mean
A basket contains 12 black marbles, 14 red marbles and 12 green marbles. What is the probability of picking a black marble first then a red marble as replacement?
Use the following cell phone airport data speeds (Mbps) from a particular network. Find
Upper Q 1
.
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.5
0.5
0.6
0.7
0.8
0.8
0.8
0.9
1.2
1.2
1.2
1.4
1.7
1.8
2.1
2.6
2.9
2.9
2.9
3.1
3.2
4.3
5.4
5.6
5.8
7.2
7.6
7.8
7.9
8.1
8.2
10.3
11.3
12.2
12.9
13.6
13.9
14.7
15.3
15.4
15.5
15.7
28.8
Upper Q 1
