Jen observed that 91% of the background checks he processes are for potential employees who have already interviewed. Let X be the number of background checks Jen processes to get his first background check for a potential employee who has not yet interviewed for the job. Assume that the interview statuses are independent.

(a) Find the probability that the 2nd background check that Jen processes is the first for which the potential employee has not yet interviewed.

(b) What is the underlying process for the random variable X?

(c) Suppose Y is the number of potential employees who have already interviewed in a group of 15 employees. How are X and Y different?

Q. We have a recombinant inbred line population in the F10 generation (NOTE THAT THIS IS A RECOMBINANT INBRED POPULATION (RIL), NOT AN F2 POPULATION). In this population, it was observed that there were 62 RILs with purple flowers and 38 RILs with white flowers.

1. What is the expected number of individuals for each class if a single dominant gene conditions purple flower color? For example, the parents used to produce the RIL population could be WW x ww.

2. Calculate the Chi-square statistic for this expected ratio.

3. Does the observed number of purple vs white fit the expected ratio for a single dominant gene at the 0.05 level of probability?

According to the National Eye Institute, 8% of men are red-green colorblind. A sample of 125 men is gathered from a particular subpopulation, and 13 men in this sample are colorblind.(Without using z-value)

a. Is this statistically significant evidence that the proportion of red-green colorblind men is greater than the subpopulation than the national average with alpha = 0.05?

b. What is the maximum number of men that could have been colorblind in this sample that would lead you to fail to reject the null hypothesis?

c. Using 8% as the probability of being colorblind, find a 95% confidence interval for the number of men in a sample of 125 who are colorblind.

An exam has 5 questions and each of them has 4 possible answers. A student gets 3 points
for each correct answer and loses 1 point for each wrong answer. Consider a student who
answers all questions completely at random. Let X denote the number of correct answers and
Y the number of points of this student at the end of the test. (A negative score is possible).
(a) Compute the mean and the standard deviation of Y , µY and σY .
(b) Compute P(µY − σY ≤ Y ≤ µY + σY ) and P(µY − 2σY ≤ Y ≤ µY + 2σY ).
(c) What is the probability that the student above gets a positive score?

1. A box contains six 25-watt light bulbs, nine 60-watt light bulbs, and five 100-watt light bulbs. What is the probability a randomly selected a 60 watt light bulb? (PLease explain how did you get your answer)(2 pt) Note: You must provide your answer as a fraction NOT decimal)

2. Cell Phone Provider	Probability
   AT&T	0.271
   Sprint	0.236
   T–Mobile	0.111
   Verizon	0.263

   Does the above table represent the probability model? Explain your answer. (2 pt)

3. The data shows the distance that employees of a certain company travel to work. One of these employees is randomly selected. Determine the probability that the employee travels between 10 and 29 miles to work. (2 pts)

   Distance (miles)	Number of employees
   0 – 9	124
   10 – 19	309
   20 – 29	257
   30 – 39	78
   40 – 49	2

4. In Q3, Is the probability the employee travels between 40 and 49 miles to work considered to be unusual? Explain your answer. (2 pt)

5. The probability that a randomly selected murder resulted from a rifle or shotgun is

   P(rifle or shotgun) = 0.059. Interpret this probability. (2 pt)

   Choose one of the correct answers from below.

   A. If 1000 murders were randomly selected, we would expect about 59 of them to have resulted from a rifle or shotgun.
   B. If any person is randomly selected, there is a 59 % chance the person will be murdered with a rifle or shotgun.
   C. If any person is randomly selected, there is a 5.9% chance the person will be murdered with a rifle or shotgun.
   D. If 1000 murders were randomly selected, exactly 59 of them would have resulted from a rifle or shotgun.

Of all the infectious diseases that affect humans, which one would you rank as the highest priority for eradication? What factors influence your preference? What would be required to actually eradicate your selected infectious disease?

Assuming a discount rate of 6 percent, which of the following has the highest cash value (present value at the date of purchase)? Assume all purchase options below are as at the same date. There will be a single cash flow for all of the alternatives (balloon payments at the end of the financing period).

a. $90,000 in 3 years

b. $60,000 today

c. $120,000 in 8 years

d. $100,000 in 5 years

For a growing firm, which depreciation method results in the highest return on assets (ROA)?

Group of answer choices

A) Double declining balance.

B) Straight line.

C) ROA is the same under all methods.