1-For Continuous Random Variables We CANNOT Find Probabilites for Exact Outcomes

1-For continuous random variables we CANNOT find probabilites for exact outcomes.

Select one:

True

False

2-Sally is going to play a simple game. There are 10 blocks in a box, 5 red = R, 3 yellow = Y and 2 blue = B.

Sally without looking will randomly pick a block; if the block is red she flips a coin, heads (H) she wins tails (T) she loses. If she picks a yellow block she automatically loses. If she picks a blue block she automatically wins.

◦Answer the following questions about the sample space and probabilities of the game.

◦A good organized approach is to use the example of the tree diagram on Pages 241 and 242.

1-8/10

2- 3/10

3-RH RT YH YT BH BT

4-5/20+2/10=9/20

5- Y B H T

6- 7/10 + 1/20=15/20

7-3/10 + 2/20= 8/20

8-5/20 + 3/10= 11/20

9- 5/20= ¼

10- RH RT Y B

11- ARE MUTUALLY EXCLUSIVE

3-For each situation, is the given percent a statistic or a parameter?

Of 10 students sampled from a class of 200, 8 (80%) said they would like the school library to have longer hours.

75% of all students at a school are in favor of more bicycle parking spaces on campus.

A customs inspector sampled 5 boxes among 20 boxes being shipped from out of the country. He found that one of the five boxes (20%) contained an illegal food item.

Based on the 2000 Census, 39.5% of the California population of residents who are over 5 years old speak languages other than English at home.

4- Many undergraduate students are thinking about getting a graduate degree. What proportion of US undergrads is this? A properly conducted random survey of undergraduate students at US universities revealed that out of 265 students,

131 were seriously thinking about applying to graduate school.

What is the research question for this scenario?

Answer:

5-What is the parameter of interest (answer in words)?

Answer:

6-What is the symbol for the correct answer to the previous question?

Select one:

μ

μ1 - μ2

μd

p

p1 - p2

x-bar

xbar1 - xbar2

d-bar

p-hat

p-hat1 - p-hat2

7-What is the correct symbol for the sample statistic used to estimate the parameter for this question?

Select one:

μ

μ1 - μ2

μd

p

p1 - p2

x-bar

xbar1 - xbar2

d-bar

p-hat

p-hat1 - p-hat2

8-What is the value of the sample statistic for this question? Answer in decimal form, rounding to 3 places after the decimal if necessary.

Answer

9-We wish to find the mean volume of soda a manufacturer puts in the bottles it sells. A simple random sample of 500 bottles has a mean volume of 1.03 liters.

What is the research question for this scenario?

Answer:

10-What is the parameter of interest (answer in words)?

Answer:

11-What is the symbol for the correct answer to the previous question?

Select one:

μ

μ1 - μ2

μd

p

p1 - p2

x-bar

xbar1 - xbar2

d-bar

p-hat

p-hat1 - p-hat2

12-What is the correct symbol for the sample statistic used to estimate the parameter for this question?

Select one:

μ

μ1 - μ2

μd

p

p1 - p2

x-bar

xbar1 - xbar2

d-bar

p-hat

p-hat1 - p-hat2

13-What is the value of the sample statistic for this question? Answer in decimal form, rounding to 3 places after the decimal if necessary.

Answer:

14-Referring to the soda manufacturer, suppose we take a second simple random sample of 500 bottles. For each of the following, could the value change for a second sample taken in the exact same manner? Answer Yes (might change) or No (could not change).

The population mean volume of soda.

The sample mean volume of soda.

The population standard deviation of the volume of soda.

The sample standard deviation of the volume of soda.

15- A researcher is trying to find out which of two pain killers, P or V, is more effective for pain relief after oral surgery. A completely randomized double-blinded study is conducted, with 250 patients receiving P and 250 patients receiving V after oral surgery. The mean pain reduction for patients receiving P was 4.5 on a ten-point scale, and the mean pain reduction for patients receiving V was 4.7.

What is the research question for this scenario?

Answer:

16-What is the parameter of interest (answer in words)?

17- What is the symbol for the correct answer to the previous question?

Select one:

μ

μ1 - μ2

μd

p

p1 - p2

x-bar

xbar1 - xbar2

d-bar

p-hat

p-hat1 - p-hat2

18-What is the correct symbol for the sample statistic used to estimate the parameter for this question?

Select one:

μ

μ1 - μ2

μd

p

p1 - p2

x-bar

xbar1 - xbar2

d-bar

p-hat

p-hat1 - p-hat2

19-What is the value of the sample statistic for this question? Answer in decimal form, rounding to 3 places after the decimal if necessary.

Answer:

20-Engineers who design aircraft want to know whether a new type of lightweight bolt will survive repeated extreme temperature variation better than the type of bolt currently used. The engineers expose both types of bolts to simulations of ten years’ worth of extreme temperature variation. They find that 975 out of 1,000 of the new bolts survived, while 985 out of 1,000 of the current bolts survived.

What is the research question for this scenario?

Answer:

21-What is the parameter of interest (answer in words)?

22-What is the symbol for the correct answer to the previous question?

Select one:

μ

μ1 - μ2

μd

p

p1 - p2

x-bar

xbar1 - xbar2

d-bar

p-hat

p-hat1 - p-hat2

23-What is the correct symbol for the sample statistic used to estimate the parameter for this question?

Select one:

μ

μ1 - μ2

μd

p

p1 - p2

x-bar

xbar1 - xbar2

d-bar

p-hat

p-hat1 - p-hat2

24-What is the value of the sample statistic for this question? Answer in decimal form, rounding to 3 places after the decimal if necessary.

Answer

25- All normally distributed curves are symmetrical

Select one:

True

False

26-All symmetrical curves are normally distributed.

Select one:

True

False

27- The shape of the standardized normal distribution curve is:

Select one:

a. B ( 0, 1 )

b. Not listed here

c. N ( 0, 0 )

d. N ( 0, 1 )

e. N ( 1, 0 )

28-Find the probabilities for these Z scores. The scores were found using the TI graphing calculator. If you use the table of standardized Z scores, your answer will be close, therefore find the closest value.

I highly recommend reading the lesson on finding the Z scores using the TI graphing calculator, which is posted in our Moodle class.

Choose one for the above Q

1-three standard deviations of the mean

2-two standard deviations of the mean

3-= .050

4-= .048

5- P ( Z> + X)

6-=.945

7- 1- P (Z> +X)

8-=.982

9-= .018

10-= P ( Z≤ 0 ) = .50

11-one standard deviation of the mean

29-The binomial experiment is defined by which of the following characteristics?

Select one or more:

a. The outcomes are independent of each other

b. The probability of success can vary and is found following a long number of trials, we call this the "long run".

c. The outcomes are mutually exclusive

d. The probability of success is fixed and remains the same for each trial

e. There are many trials determined once the experiment is completed

f. Newer textbooks state there are actually three possible outcomes; "success", "failure" and "not applicable"

g. There are many outcomes which cannot be determined until the experiment is completed

h. The shape of the sampling distribution is always "bimodal".

i. There are two possible outcomes; success or failure

j. There are a fixed number of trials determined in advance of the experiment

30-A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company's claim is correct, what is the expected number of nondefectivelightbulbs in a random sample of 1,000 bulbs?

Select one:

20

200

960

980

1,000

31-The costs of all the repair jobs at a large muffler repair shop produces a mean of $127.95 and a standard deviation of $24.03. If a business analyst takes simple random samples of 40 of this shop's repairs and computes the sample mean over and over again, what will be the mean and standard deviation of these sample means?

Select one:

Mean $3.20, standard deviation $0.60

Mean $3.20, standard deviation $3.80

Mean $3.20, standard deviation $24.03

Mean $20.23, standard deviation $0.60

Mean $20.23, standard deviation $3.80

Mean $20.23, standard deviation $24.03

Mean $127.95, standard deviation $0.60

Mean $127.95, standard deviation $3.80

Mean $127.95, standard deviation $24.03

32-A fair coin is flipped 10 times and the number of heads is counted. This procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?

Select one:

Choice (A)

Choice (B)

Choice (C)

Choice (D)

Choice (E)

33-Julie generates a sample of 20 random integers from 1 through 10 inclusive. She records the proportion of 6's in the sample. For example, if she had three 6's in her sample she would have recorded the value 3/20 or 0.15.

Julie repeats her process 99 more times, recording the proportion of 6's in each sample. What kind of distribution has she simulated?

Select one:

The sampling distribution of the sample proportion with n = 20 and p = 0.1.

The sampling distribution of the sample proportion with n = 20 and p = 0.6.

The binomial distribution with n = 20 and p = 0.1.

The binomial distribution with n = 100 and p = 0.1.

The binomial distribution with n = 20 and p = 0.6.

34-Big Town Fisheries recently stocked a new lake in a city park with 2,000 fish of various sizes. The distribution of the lengths of these fish is approximately normal.

Big Town Fisheries claims that the mean length of the fish is 8 inches. If the claim is true, which of the following would be more likely?

A random sample of 50 fish having a mean length that is greater than 10 inches

A random sample of 15 fish having a mean length that is greater than 10 inches

Suppose the standard deviation of the 2,000 fish in the lake is 2.1 inches. If the mean length of the fish is 8 inches, use the normal distribution to compute the probability that a random sample of 50 fish will have a mean length less than 7.5 inches. Round to three places after the decimal.

Answer

35-Suppose the distribution of fish lengths in this lake was not normal, but still had mean 8 inches and standard deviation 2.1 inches. Would it still be appropriate to use the normal distribution to compute the probability in the last question? Justify your answer.

Answer: