Question 4:Use the two-way table below to answer the questions that follow.

	Level of Technical Writing Expertise
None	Beginner	Intermediate	Expert
Major	Natural Sciences	8	7	11	39
Social Sciences	11	41	13	9
Humanities	9	11	25	19
Interdisciplinary	15	9	21	14

1. What is the probability of randomly selecting a social sciences major or an intermediate level technical writer? (2 points)

1. What is the probability of selecting a Humanities major? (2 points)

1. What is the probability of randomly selecting an expert level technical writer given the student is a natural sciences major? (3 points)

1. What is the probability of selecting a natural sciences major given the students is an expert level technical writer? (3 points)

Question 5:The table below summarizes pets owned by students in a class.

Pet Type	Relative Frequency
Cat/Dog	0.61
Snake/Lizard	0.12
Hamster/Gerbil/Rat	0.08
Bird	0.04
Other	0.10
None	0.30

State two reasons why the table given is not a probability distribution. (4 points)

Question 6:The sample space for flipping 3 coins is given below.

{HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

1. Let X = the number of tails flipped. Find the probability distribution for Xby completing the table below. (3 points)

X	P(X)

1. Find and interpret P(X = 0). (2 points)

1. Find and interpret P(X 2). (2 points)

1. Find E(X). (3 points)

Question 7:38% of the adult US population has prediabetes. Suppose a sample of 200 adults is selected. Use this information to answer parts (a) through (h).

1. The number of adults in the random sample of 200 is binomially distributed. Mark all statements below that correctly describe why this random variable is binomial. (4 points)

____ The probability of getting an adult with prediabetes is the same throughout all the trials.

____ The probability of getting an adult with prediabetes on a given trial depends on the outcomes of the previous trials.

____ There is a fixed number of trials.

____ Each person sampled either does or does not have prediabetes.

____ Whether one individual has or does not have prediabetes is independent of the other trials.

1. State the values of n and pfor the binomial distribution. (3 points)

1. Find and interpret P(X 70). (3 points)

1. Find the probability of getting at least 75 adults having prediabetes. (2 points)

1. Suppose a sample of 200 adults had 92 having prediabetes. Using probability, determine if this is a significantly high number of adults having prediabetes. (3 points)

1. Find the mean and standard deviation of the binomial distribution. (3 points)

1. Using the range rule of thumb, find the lower and upper boundaries for values that separate significantly low and high values from those that are not significant. (3 points)

1. Using the range rule of thumb, would a sample containing 55 people having prediabetes be considered significantly low? (2 points)

Question 8:Write the probability statement that the graph below depicts by filling in the boxes. (3 points)

Question 9:Use the standard normal distribution calculator to answer each question that follows. (2 points each)

1. Find P(Z -0.5)

1. Find P(1.5 Z 2).

1. Find the z-score that represents the 40^th percentile.

1. Find the critical value .

Question 10:Consider the critical value . Select the graph below that accurately depicts this critical value. (3 points)

A.	B.
C.	D.

Question 11:Scores on a recent test were normally distributed with a mean of 77 and a standard deviation of 7. (2 points each)

1. What proportion of scores were between 80 and 90?

1. What score represents the 90^th percentile?

1. What two scores bound the middle 50% of scores?

1. What z-score corresponds to a test score of 61? Is this score significantly low?

Question 12:At a soda bottling plant, cans of cola are supposed be filled with 12 ounces of soda. Due to random fluctuations in the filling process, it is found that the volume of soda in a randomly selected can is normally distributed with a mean of 12 ounces and standard deviation of 0.143 ounces.

1. A quality control technician is checking whether the machine is overfilling the cans. If one can is randomly selected, what is the probability it contains 12.03 ounces or more? (2 points)

1. The quality control technician selects a random sample of 100 cans and calculates the mean volume of the sample of cans. What is the probability that the mean volume of the 100 cans is 12.03 ounces or more? (4 points)

1. Suppose the quality control technician does obtain a sample of 100 cans having a mean volume of 12.03 ounces. Should the technician conclude the machine is functioning properly, or does it appear that the machine is overfilling the cans? Explain your answer using the probability you found in part (b). (5 points)