Which of the following statements are TRUE?

Note that there may be more than one correct answer; select all that are true.

There are countably infinite values of X in a continuous uniform distribution.

For a continuous uniform distribution defined on the interval [a,b], P(X < a) and P(X > b) is undefined.

The mean and the variance of a continuous uniform random variable are the same.

In a continuous uniform distribution, the mean and the median are the same.

In a continuous uniform distribution, the height of the curve, f(x), is the same for all values of the random variable X.

1a) Assume we're working with normally distributed SAT scores, with the following distribution: Mean = 500 and Std. Dev = 100. A student is randomly selected from the SAT population. What's the probability of that student's score being between 350 and 600?

1b) Assume we're working with normally distributed SAT scores, with the following distribution: Mean = 500 and Std. Dev = 100. A college decides to admit students with SAT scores greater than or equal to 450. Assuming the applicant population contains 1500 students, how many would be admitted?

1c) Assume we're working with normally distributed SAT scores, with the following distribution: Mean = 500 and Std. Dev = 100. A college decides to admit only the top 10% of SAT students. What would its cutoff SAT score be?

The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 1 in every ten thousand. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms

The following table contains observed frequencies for a sample of 200.

Test for independence of the row and column variables using a= .05

Compute the value of the  test statistic (to 2 decimals).

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard deviation 4 inches.

(a) What is the probability that an 18-year-old man selected at random is between 71 and 73 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of thirty 18-year-old men is selected, what is the probability that the mean height x is between 71 and 73 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution.    

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

Using the unit normal table, find the proportion under the standard normal curve that lies to the right of the following values. (Round your answers to four decimal places.)

(b) z = −1.05

(c) z = −2.40

The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = 0.000786 mm. Assume a random sample of 55 sheets of metal resulted in an x¯ = 0.3307 mm. Calculate the 98 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.) The 98% confidence interval is from to

Suppose five bananas and seven oranges are placed in a fruit basket.

A. Suppose three fruits are chosen with replacement, sketch a tree diagram that shows all possible outcomes.

B. If three fruits are chosen at random with replacement find the probability that at least one banana is drawn.

C. If all three of the chosen foods are the same type what is the probability they’re all are bananas.

Suppose five bananas and seven oranges are placed in a fruit basket.

A. Suppose three are chosen without replacement sketch a tree diagram that shows all possible outcomes.

B. Add three fruits are chosen at random without replacement find the probability that the second group is an orange regardless of other draws .

C. It’s all three of the chosen fruit are the same type what is the probability they’re all oranges?

For three events A, B, and C, we know that

• A and C are independent,
• B and C are independent,
• A and B are disjoint,

Furthermore, suppose that ?(?∪?)= 2/3, ?(?∪?)=3/4,?(?∪?∪?)=11/12.

Find ?(?), ?(?), and ?(?).

In how many ways can 7 people { A, B, C, D, E, F, G } be seated at a round table if

(a) A and B must not sit next to each other;

(b) C, D, and E must sit together (i.e., no other person can sit between any of these three)?

(c) A and B must sit together, but neither can be seated next to C or D.

Consider each of these separately. For (c) you may NOT simply list all possibilities, but must use the basic principles we have developed (you may check your work with a list if you wish).

Hint: Conceptually, think of the groups of two or three people as one "multi-person" entity in the overall circular arrangement. However, a "multiperson" is an unordered entity, and you will have to think about how many ways a "multiperson" could be ordered. It may help to draw a diagram, fixing a particular person at the top of the circle (thereby eliminating the duplicates due to rotations).

The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.

43    41 39 39 38 37 37 36 34 33 33 32

The lower limit for determining outliers for a box-and-whisker plot is ________.

23.75

20.0

22.5

25.25

The two data sets in the table below are dependent random samples. The population of (x−y)(x-y) differences is approximately normally distributed. A claim is made that the mean difference (x−y)(x-y) is not equal to -23.5.

For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.

(a) Calculate the value of the test statistic used in this test.

     Test statistic's value =

(b) Use your calculator to find the P-value of this test.

     P-value =

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.04 significance level. If there are two critical values, then list them both with a comma between them.

     Critical value(s) =

(d) What is the correct conclusion of this hypothesis test at the 0.04 significance level?     

• There is not sufficient evidence to support the claim that the mean difference is not equal to -23.5
• There is sufficient evidence to warrant rejection the claim that the mean difference is not equal to -23.5
• There is not sufficient evidence to warrant rejection the claim that the mean difference is not equal to -23.5
• There is sufficient evidence to support the claim that the mean difference is not equal to -23.5

The following contingency table shows the number of two-bedroom apartments grouped by monthly rent and location.

Monthly Rent                      York       Lancaster      Dover              Total
$600 to under $700              6              15                     9                      30
$700 to under $800              30                  21                   24                     75
$800 to under $900             15                  18                    12                      45
Total   51                   54                   45                     150

The probability that a randomly selected apartment from this group has a monthly rental from $700 to under $800 or is located in Lancaster is ________.