8) Match each definition with the term it defines. You may use terms once, more than once, or not at all. If all of your answers are correct, a clue will appear.

A. Variance
B Dependent
C. Residual plot
D. Independent
E. Mutually exclusive
F. Correlation coefficient G. Simple random sample H. Permutation
I. Z-score

J. Normal distribution
K. Student’s t distribution
L. Tukey-Kramer test
M. Discrete
N. Continuous
O. Skewed to the left
P. Chi-square goodness-of-fit test Q. Confidence Interval
R. One-way ANOVA

S. Combination
T. Binomial experiment U. Relative Frequency
V. Cumulative Frequency W. Null hypothesis
X. Alternative hypothesis Y. Skewed to the right
Z. Symmetric

____ A subset of a population in which each member of the population has an equal probability of being included

____ Two events are ______________ if they cannot occur at the same time.

____ Experiment with a fixed number of independent trials, each with exactly 2 outcomes and the same probability of success

____ Used to test the hypothesis that several population means are all equal

____ The number of standard deviations that a value falls above or below the mean

____ Two events are ______________ if the occurrence of one does not affect the probability of the other.

____ If x̄ is much smaller than the median, the distribution is most likely this shape.

____ Numerical measure of the strength and direction of a linear relationship between two variables

____ When two variables have a linear relationship, the ____________ will not exhibit any noticeable pattern.

____ The number of ways that a group of items can be ordered

____ ? − ? ?

____ A collection of objects in which the order doesn't matter
____ A range of values that is likely to include an unknown parameter
____ Frequency of a class divided by the sum of all frequencies
____ Measure of how far, on average, the values in a data set are from the mean ____ The test statistic for this procedure follows the F-distribution.
____ Events A and B are ___________________ if P(A and B) = 0.

Location(s) eliminated:

1. The manager of a bar and grille in Dallas has been gathering data on the number of minutes a  

    party of four spends in the restaurant from the moment they are seated to when they pay the

    check. Round all values to the 4^th decimal place SHOW WORK INCLUDING FORMULA USED

1. Calculate the mean number of minutes (E(x)) for a dinner party of four.
2. What is the variance and standard deviation?

____________________________________________________________________________

Number of Minutes   Probability

            x                            P(x)                x P(x)                  x - E(x)                     (x – E(x))² P(x)

   ____________________________________________________________________________    

         60                           0.30       

           70                           0.20                                                                                             

           80                           0.15       

           90                           0.35      

_____________________________________________________________________________

                    E(x) = ∑ [xP(x)] =                                   σ² =∑ [(x – E(x))² P(x)] =

1. E(x) = ∑ [xP(x)] =

2. Variance, σ² =∑ [(x – E(x))² P(x)] =

3. Standard deviation, σ =

A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty randomly selected fish are placed in a tank containing this concentration of chemical in water. a. Demonstrate that X is a binomial random variable where X is the number of fish that survive. _____________________________________________ _____________________________________________ ___________________________________________(3) Find the following probabilities: b. More than 10 but at most 15 will survive. ______________________________(2) c. Exactly 10 will survive. ______________________________(2) d. At least 8 but less than 12 will not survive. ______________________________(2) e. More than 9 but less than 16 will not survive. _____________________________(2) f. What is the mean number of fish that will survive? Use the correct notation. _____________________________(3) g. What is the standard deviation for this probability distribution? Use the correct notation. _____________________________(3) h. Find ?(µ +  > X) for X = the number of fish that survive. ________________

In a sample of families with 6 children each, the distribution of boys and girls is as shown in the following table:

Part A) Calculate the chi-square value to test the hypothesis of a boy-to-girl ratio of 1:1. (Express your answer using three decimal places)

Part B) Are the numbers of boys to girls in these families consistent with the expected 1:1 ratio? Yes or No

Part C) Calculate the chi-square value to test the hypothesis of binominal distribution in six-child families. (Express your answer using three decimal places)

Part D) Is the distribution of the numbers of boys and girls in the families consistent with the expectations of binomial probability? Yes or No

1A) Calculate the values of expected return for the stock fund. (Do not round intermediate calculations. Enter your answer as a decimal number round to 3 decimal place.)

1B) Calculate the values of variance for the stock fund. (Do not round intermediate calculations. Enter your answer as a decimal number round to 4 decimal place.)

1C) Calculate the value of the covariance between the stock and bond funds. (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a decimal number rounded to 5 decimal places.)

A cinema has a single ticket counter that is manned by a cashier. The cashier is capable to handle 280 customers in an hour. Customers arrive at the counter at the rate of four customers per minute. Daniel, the owner who studied queuing models feels that all the seven assumptions for a single-channel model are met. By assuming Exponential service times and Poisson arrival rate, answer the following questions.

a) State three assumptions mentioned above.

b) Determine the average number of customers waiting to buy ticket.

c) Determine the percentage of time the cashier is free.

d) Calculate the average time spent by each customer in the system.

e) Calculate the average time each customer needs to spend waiting to buy ticket.

f) The management of the theatre is planning to increase the number of counters if the probability of the system is busy is higher than 0.5. Is it necessary to increase the number of counters?

For a healthy human, a body temperature follows a normal distribution with Mean of 98.2 degrees Fahrenheit and Standard Deviation of 0.26 degrees Fahrenheit. For an individual suffering with common cold, the average body temperature is 100.6 degrees Fahrenheit with Standard deviation of 0.54 degrees Fahrenheit. Simulate 10000 healthy and 10000 unhealthy individuals and answer questions 14 to 16.

14. If person A is healthy and person B has a cold, which of the events are the most likely? Pick the closest answer.

• a. Person B will have higher temperature than 101 degrees.
• b. Person A will have temperature higher than 99 degrees
• c. Person B will have temperature lower than 100 degrees
• d. ​​Person A will have temperature lower than 97.5 degrees

15. What would be a range [A to B], which would contain 68% of healthy individuals? Pick the closest answer.

• a. Between 97.9 and 98.46
• b. Between 99.5 and 101.6
• c. Between 100.06 and 101.14
• d. Between 100.1 and 102.2

16. What is the approximate probability that a randomly picked, unhealthy individual (one with the cold) would have body temperature above 101 degrees Fahrenheit? Pick the closest answer.

• a. About 10%
• b. About 15%
• c. About 22%
• c. About 34%

A random experiment was conducted where a Person A tossed five coins and recorded the number of “heads”. Person B rolled two dice and recorded the sum the two numbers. Simulate this scenario (use 10000 long columns) and answer questions 10 to 13.

10. Which of the two persons (A or B) is more likely to get the number 4?

• a. Person A
• b. Person B
• c. Not possible to determine

11. Which of the two persons will have higher Median among their outcomes?

• a. Person A
• b. Person B
• c. Not possible to determine

12. What is the probability that person B obtains number 5 or 6?

• a. About 15%
• b. About 25%
• c. About 35%
• c. About 55%

13. Which of the persons has higher probability of getting the number 3 or smaller?

• a. Person A
• b. Person B
• c. Not possible to determine

Every morning Mary randomly decides on one of three possible ways to get to work. She makes her choice so that all three choices are equally likely. The three choices are described as follows: • Choice A (Drives the highway): The highway has no traffic lights but has the possibility of accidents. The number of accidents on the highway for the hour preceding Mary’s trip, X, follows a Poisson distribution with an average of 2. The time (minutes) it takes her to get to work is affected by the number of accidents in the hour preceding her trip due to clean up. The time (in minutes) it takes her is given by T = 54.5 + 5X. • Choice B (Drives through town): Suppose there is no possibility of being slowed down by accidents while going through town. However, going through town she must pass through 10 traffic lights. Suppose all traffic lights act independently from one another and for each there is a probability of 0.5 that she will have to stop and wait (because it is red). Let Y be the number of lights she will stop and wait at. The time (in minutes) it takes her is given by T = 58.5 + Y. • Choice C (Takes the train): Trains arrive for pick-up every 5 minutes. If the train has room, it will take her exactly 50 minutes to get to work. If an arriving train is full she will have to wait an additional 5 minutes until the next train arrives. Trains going through the station will arrive full with probability 0.75, and thus she cannot get on and will have to wait until the next train. Suppose it takes Mary exactly 5 minutes to get to the train station and she always arrives at the station just as a train arrives. Let Z be the number of trains she’ll see until she can finally board (the train isn’t full). The time (in minutes) it takes her is given by T = 50 + 5Z.

a) Which choice should she make every morning to minimize her expected travel time?

b) On one morning Mary starts her journey to work at 7am. Suppose it is necessary that she is at work at or before 8:00 am. Which route should she take to maximize the probability that she is at work at or before 8:00am?

A statistical program is recommended.

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for one full season.

(a)

Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt. (Round your numerical values to one decimal place. Let x₁ represent Yds/Att and y represent Win%.)

ŷ =

(b)

Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt. (Round your numerical values to the nearest integer. Let x₂ represent Int/Att, and y represent Win%.)

ŷ =

(c)

Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt. (Round your numerical values to the nearest integer. Let x₁ represent Yds/Att, x₂ represent Int/Att, and y represent Win%.)

ŷ =

(d)

The average number of passing yards per attempt for a certain team was 6.3 and the number of interceptions thrown per attempt was 0.036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the team. (Round your answer to one decimal place.)

%

For this season the team's record was 7 wins and 9 losses. Compare your prediction to the actual percentage of games won by the team.

The predicted value is lower than the actual value.The predicted value is identical to the actual value.    The predicted value is higher than the actual value.