Statistics and Probability Answers

The daily income of bank auditors in SSS Commercial Bank is normally distributed with a mean of 675 and a standard deviation of 45. What is the z-value for the income x of a bank auditor who earns 700 daily?

The average weight of 50 senior high school students is 52 kg with a standard deviation of 2.5

kg. If 25 students are randomly selected, find the mean, standard deviation, and variance of the

corresponding sampling distribution of the sample means

Graph and find the area under the normal curve from z=0 to z=2.25

Two balls are dawn in succession without replacement from an urn containing 5 Green Balls and 6 Yellow Balls.Let Y represent the Yellow Balls and G represent the Green Balls.If we let Z be the random variable representing the number of Green Balls,find the values of the random variable X.

The pulse rates of adult men approach a normal distribution with a mean of 80 bpm(beats per minute) with standard deviation of 7 bpm. If 60 bpm to 100 bpm is known to be normal. How many percent of the adults have above or below normal pulse rates?

The average length of time for students to register in the second semester at a certain university has been 70 minutes. A new registration procedure is being tested. If a random sample of 15 students have an average of 45 minutes with a standard deviation of 30 minutes under the new system, can you conclude that the new system is faster than the old one? Assume that the average length of time is normally distributed. Use α=0.05.

The two most common type of errors made by programmers are syntax errors and errors in logic. For a simple language such as BASIC the number of such errors is usually small. Let X denote the number of syntax errors and Y the number of errors in logic made on the first run of a BASIC program. Assume that the joint density for (X,Y) is as shown in table 2:

x/y

0

1

2

3

0

.400

.100

.020

.005

1

.300

.040

.010

.004

2

.040

.010

.009

.003

3

.009

.008

.007

.003

4

.008

.007

.005

.002

5

.005

.002

.002

.001

a. Find the probability that a randomly selected program will have neither of these types of error.

b. Find the probability that a randomly selected program will contain at least one syntax error and at most one error of logic.

c. Find the marginal densities for X and Y

d. Find the probability that a randomly selected program contains at least two syntax errors.

e. Find the probability that a randomly selected program contains one or two errors in logic.

Let X denote the time in hours needed to locate and correct a problem in the software that governs the timing of traffic lights in the downtown area of a large city. Assume that X is normally distributed with mean 10 hours and variance 9.

a. Find the probability that the next problem will require at most 15 hours to find and correct.

b. The fastest 5% of repairs take at most how many hours to complete?

In an automobile plant two tasks are performed by robots. The first entails welding two joints; the second, tightening three bolts. Let X denote the number of defective welds and Y the number of improperly tightened bolts produce per car.

Table 1:

x/y 0 1 2 3

0 .840 .030 .020 .010

1 .060 .010 .008 .002

2 .010 .005 .004 .001

Use table 1 to find each of these probabilities,

a. The probability that exactly two defective welds and one improperly tightened bolt will be produced by the robots.

b. The probability that at least one defective weld and at least one improperly tightened bolt will be produced.

c. The probability that at most one defective weld will be produced.

A sample of raw scores of Grade 11 students consists of the five numbers 10, 14, 17, 20 and 12. Consider samples of size 2 that can be drawn from this sample.

How many are the possible outcomes? *

What is the probability of getting 14.5 as a mean? *

What is the probability of getting 11 as a mean? *

What is the probability of getting 22.5 as a mean? *

What is the probability of getting 16 as a mean? *