Color blindness is the decreased ability to see colors and clearly distinguish different colors of the visible spectrum. It is known that color blindness affects 11% of the European population. A sample of 12 subjects is taken for research purposes by a team of optometrists.

What is the probability that one subject is color blind?

What is the probability that more than one subject is color blind?

What is the probability that at most 3 subjects are color blind?

What is the probability that the number of color blind subjects is between 2 and 4 (both included)?

What is the probability that at least 10 subjects are not color blind?

Let A and B two events defined on a sample space . Show that A and B

are independent if and only if their characteristic functions 1A and 1B are independent random variables.

b. An investor wants to create a portfolio of three stocks form a set that consists of 5 defense companies, 4 transportation companies and 6 healthcare companies. If the investor picks the three stocks at random, what is the probability that all three stocks will be from different industries.

c. In part (b), what is the probability that at least two out of the three stocks picked will be from different industries?

Four servers are currently busy, each serving a different customer. You are the next in line to be served, as soon as one server becomes available. The servers have different levels of experience, resulting in slightly different expected service time per customer. Server 1 has mean service time 50 seconds, Server 2 has mean service time 55 seconds, Server 3 has mean service time 60 seconds, and Server 4 has mean service time 65 seconds. All servers have their service time exponentially distributed. A) Determine the probability that you will be served by Server i, for i=1,2,3,4. B) Determine the expected time that you have to wait before being served. C) Determine your own expected service time (in seconds), when you are still waiting in queue (so you do not know yet which server will be assigned to you). D) Determine the total time that you expect to spend waiting and then being served.

4. For random variable X with unknown variance let S_x^2=49,x ̄=8,n=25,"and" α=0.10. Conduct the following tests. Make sure you state the decision rule and the inference.

a) H_0:μ<7H_A:μ≥7

b) H_0:μ>10H_A:μ≤10

c) H_0:μ=3H_A:μ≠3

d) Give a 90% confidence interval around .

Vishnu is headed to a the world golf championship, which has a total of  90 players. 17 players are from the United States, 36 are French, and 37 are Canadian. To gauge the talent of the event Vishnu invites ten players randomly chosen for a practice round.

a. What is the probability that the practice group contains exactly 1 player from the united states, 5 Frenchmen, and 4 Canadians?

b. What is the probability that 1 of the players selected to participate in the practice round is from the United States?

c. What is the probability that Vishnu sits with the best player at dinner after the practice round if the table is round and seating is random? (assume Vishnu is not the best player)

When summarizing scale variable data using descriptive statistics, what do we lose in our understanding of a sample if we just report the mean and not any measures of dispersion like range or standard deviation? How does this question apply to a variable like age or test scores?

Using the Grubb's test, decide whether the value 217 should be rejected from the set of results 191, 217, 202, 205, 195.

A Physics teacher takes a random sample of size 5 from his students. Their marks in a written test (x)

and a practical test (y) are given in the following table.

(i) Find the product moment correlation coefficient. [3]

(ii) Test, at the 5% significance level, whether there is evidence of positive correlation. [4]

The teacher takes a second random sample, this time of size 7, and the marks for this sample are summarised as follows.

Σx=96 Σx2 =1366 Σy=86 Σy2 =1096 Σxy=1220
(iii) Use the combined sample of size 12 to find the equation of the regression line of y on x, giving

your answer in the form y = px + q, where p and q are constants. [4]

One particular student scored 13 in the written test, but was absent for the practical test.

(iv) Estimate this student’s mark in the practical test and comment on the reliability of your estimate.

1) How many different ways can you arrange the letters in the words

a) “friends”

b) “initial”

c) “probability”

Show your calculations.

A pilot study is run to investigate the effect of a lifestyle intervention designed to increase medication adherence in patients with HIV. Medication adherence is measured as the percentage of prescribed pills that are taken over a one-week observation period. Ten patients with HIV agree to participate and their medication adherence before and after the intervention are shown below. Compute the standard deviation of the difference in adherence before versus after intervention. Please show your work and explain.Thank you!

Problem 1)

Try creating 100 normally disributed random numbers with an average of 10 and standard deviation of 1. How close is the average to 10? How close is the standard deviation to 1?

Problem 2)

Try creating 100 normally disributed random numbers with a true average of 10 and true standard deviation of 1. What is the confidence interval for the measured average? Is it higher or lower than the confidence interval for 20 samples?

The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 148 feet. Use a significance level of 0.05. Height (ft) Interval after (min) 136 83 140 84 134 94 144 92 102 67 109 67 104 84 116 84

As a researcher, you will be considering the relationships between variables regularly. Linear correlation is the most basic relationship that may exist between two variables. This assignment will you give the opportunity to see how statistics can start to answer the research questions you will be faced with in your field of study.

Correlation Project Directions:

Consider a possible linear relationship between two variables that you would like to explore.

1. Define the relationship of interest and a data collection technique.
2. Determine the appropriate sample size and collect the data.
3. Perform the appropriate analysis to determine if there is a statistically significant linear relationship between the two variables. Describe the relationship in terms of strength and direction.
4. Construct a model of the relationship and evaluate the validity of that model.

Show all work to receive full credit. Provide complete sentence explanations for each of the above.

Directions: Create a PowerPoint with presenter’s notes describing your research project. A minimum of 10 slides is required, including a title and References slide. The presentation should address the following:

1. Describe the techniques and procedures that will be used.
2. State the hypothesis.
3. State general equipment that will be necessary and their intended use.
4. Describe type of data that will be collected and measurements that will be made.
5. Define and describe experimental units and be specific.
6. Define the population for generalization.
7. Define sampling technique and randomization, and include rationale.