REVIEW QUESTIONS - TOPIC 2:

Complete the following exercises, and put them into a Word document to submit to the instructor.

1. Chapter 5, numbers 5.13 and 5.14
2. Chapter 8, numbers 8.16 and 8.19

Show all relevant work; use the equation editor in Microsoft Word when necessary.

5.13) IQ scores on the WAIS test approximate a normal curve with a mean of 100 and a standard deviation of 15. What IQ score is identified with

1. (a)the upper 2 percent, that is, 2 percent to the right (and 98 percent to the left)?
2. (b) the lower 10 percent?
3. the upper 60 percent?
4. (d) the middle 95 percent? [Remember, the middle 95 percent straddles the line perpendicular to the mean (or the 50th percentile), with half of 95 percent, or 47.5 percent, above this line and the remaining 47.5 percent below this line.]
5. (e) the middle 99 percent?

5.14) For the normal distribution of burning times of electric light bulbs, with a mean equal to 1200 hours and a standard deviation equal to 120 hours, what burning time is identified with the

1. (a) upper 50 percent?
2. (b) lower 75 percent?
3. lower 1 percent?
4. (d) middle 90 percent?

8.16) A traditional test for extrasensory perception (ESP) involves a set of playing cards, each of which shows a different symbol (circle, square, cross, star, or wavy lines). If C represents a correct guess and I an incorrect guess, what is the probability of

1. (a)C?
2. (b) CI (in that order) for two guesses?
3. CCC for three guesses?
4. (d) III for three guesses?

8.19) A sensor is used to monitor the performance of a nuclear reactor. The sensor accurately reflects the state of the reactor with a probability of .97. But with a probability of .02, it gives a false alarm (by reporting excessive radiation even though the reactor is performing normally), and with a probability of .01, it misses excessive radiation (by failing to report excessive radiation even though the reactor is performing abnormally).

1. (a)What is the probability that a sensor will give an incorrect report, that is, either a false alarm or a miss?
2. (b) To reduce costly shutdowns caused by false alarms, management introduces a second completely independent sensor, and the reactor is shut down only when both sensors report excessive radiation. (According to this perspective, solitary reports of excessive radiation should be viewed as false alarms and ignored, since both sensors provide accurate information much of the time.) What is the new probability that the reactor will be shut down because of simultaneous false alarms by both the firsthand second sensors?
3. Being more concerned about failures to detect excessive radiation, someone who lives near the nuclear reactor proposes an entirely different strategy: Shut down the reactor whenever either sensor reports excessive radiation. (According to this point of view, even a solitary report of excessive radiation should trigger a shutdown, since a failure to detect excessive radiation is potentially catastrophic.) If this policy were adopted, what is the new probability that excessive radiation will be missed simultaneously by both the first and second sensors?

Helpful, additional information from the instructor below:

"Hello, Class

In this week's assignment, you need to work with standard normal distribution table.

In some exercise problems, you need to apply z score formula and then use the table.

I want to talk about 5.11( for practice) and 5.13(homework) particularly.

For a table, go to page 458-459 z table.

First, you need to round your z value to two decimal places.

I will use some numbers for example.

If our z score is 2.17, find 2.17 in column A in page 459.

Column B says 0.4850 and column C says 0.0150.

0.4850 indicates the region between 0 and 2.17.

0.0150 indicatesthe region greater than 2.17.

Now, depending on the problem, let's say we are looking at "above 2.17", then the answer is just 0.0150(proportion, probability).

If the question is below 2.17, we need to add 0.5 to 0.4850 because below 2.17 means two components, 1) between 0 and 2.17 , 2) below 0.

Please visualizethis scenario.

That is why we need to add 0.5 and 0.4850.

Depending on the problem, you need to modify the values in column B and C.

The only exception is when our z value is negative.

Our table does not show a negative z score.

Hence, we need to modify the given problem using the fact that normal distribution(z) is symmetric.

For example, if we have "below -2.17", we use "above 2.17".

If we have "above -2.17", we use "below 2.17".

It is important to visualizethe problem.

If you want %, just multiply your answer (proportion, probability) by 100%.

I hope this helps.

One more thing: if we have "between two z values" like -1.56 and 2.13,

see the column B for 1.56 and 2.13 and add them (visualize the graph).

If we have 1.56 and 2.13, then take a difference between two answers from column B.

If we have -1.56 and -2.13, you do the same using 1.56 and 2.13.

5.13 is the oppositeof 5.11 questions.

For example, lower 10% is 10th percentile.

You need to use that proportion to find a corresponding z value from the table.

Then, you need to use that z value with the mean and standard deviation to find the answer.

Since mean is 100 and standard deviation is 15, we get the following

(x -100)/15 = z, which is equivalent to x = 15*z + 100.

You just need to find z value from the table using the given information( againlower 10% is 10th percentile, find z value from the table corresponding to that proportion) and substitute for z in the equation above.

Please remember that our table does not include negative numbers because normal distribution is symmetric.

Hence, if we need any negative z value, we need to find positive z value from the table and place the negative sign in front of that.

For example, top 10 % z value is 1.28 and bottom(lower) 10% z value is -1.28."