Exam 5: Probability Distributions and Data Modeling

Use the data given below to answer the following question(s). 15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study. Respondent Gender Preference 1 Female Art.s 2 Male Science 3 Male Math 4 Female Art.s 5 Female Math 6 Male Science 7 Male Math 8 Male Math 9 Female Art.s 10 Male Art.s 11 Male Science 12 Female Science 13 Female Math 14 Male Art.s 15 Female Art.s -Use the multiplication law of probability to compute the probability that the respondent is male and prefers Math.

Use the data given below to answer the following question(s). In an event $X$ , the probability of rolling a sum of 8 on two dice is $\frac{5}{36}$ while the probability of rolling an 11 is $\frac{2}{36}$ . In another event $Y$ , the probability of rolling a 2 is $\frac{1}{36}$ , the probability of rolling a 9 is $\frac{4}{36}$ , and the probability of rolling a 4 is $\frac{3}{36}$ . -Consider an event Z that includes all outcomes of rolling two dice whose sum is odd.What is the probability that either event Y or Z occurs?

Use the data given below to answer the following question(s). On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year.(Hint: Use Poisson distribution formula). -What is the probability that exactly 13 students will take up Arts in the coming year?

Use the data given below to answer the following question(s). The profit from selling folding tables varies uniformly each quarter between $1,500 and $2,300. -What is the probability that profit will be less than $1,900?

While rolling two dice, what is the probability of rolling a sum of 7 or more?

For a discrete random variable X, which of the following computes the expected value?

John and Mike were offered mints.What is the probability that at least John or Mike would respond favorably? (Hint: Use the classical definition).

How are probability, experiment, outcome, and sample space related to each other?

Use the data given below to answer the following question(s). In an event $X$ , the probability of rolling a sum of 8 on two dice is $\frac{5}{36}$ while the probability of rolling an 11 is $\frac{2}{36}$ . In another event $Y$ , the probability of rolling a 2 is $\frac{1}{36}$ , the probability of rolling a 9 is $\frac{4}{36}$ , and the probability of rolling a 4 is $\frac{3}{36}$ . -What is probability that neither X nor Y will occur?

What is a random number? How is it generated in Excel?

The binominal distribution:

Which of the following is true about the Random Number Generation tool?

Use the data given below to answer the following question(s). At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning.The spinners each have four colored spaces - red, yellow, blue, and green.Red = 1, Yellow = 2, Blue = 3, and Green = 4 -What is the probability that the spinners land on colors summing up to exactly 3?

Which of the following is true about variance?

The Kolmogorov-Smirnov procedure:

Which of the following is true of the binomial distribution?

The VLOOKUP function in Excel can be used to generate outcomes from any discrete distribution.

Use the data given below to answer the following question(s). At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning.The spinners each have four colored spaces - red, yellow, blue, and green.Red = 1, Yellow = 2, Blue = 3, and Green = 4 -Compute the variance of the random variable that denotes the possible summed scores from the two spinners.

Use the data given below to answer the following question(s). The profit from selling folding tables varies uniformly each quarter between $1,500 and $2,300. -What is the probability that profit will be between $2,000 and $2,200?

Consider an event X comprised of three outcomes whose probabilities are $\frac{9}{18}, \frac{1}{18}, \text { and } \frac{6}{18}$ Compute the probability of the complement of the event.