I need help with my statistics work

There are 8 questions in total, each worth about 12 points. Please upload your answers to the dropbox. Work must be shown for credit. The Midterm can only be taken one time. It is not something that can be made up in the event of an Incomplete as the answers / directions are given in the feedback.

This Midterm is open book/open notes / open tables etc.. It is not meant to be completed with the help of any other individual. You may use tutors to complete similar problems to help prepare, but these exact problems are not ones that should be solved with a tutor. A zero on the midterm is the grade earned if these problems are worked with a tutor.

Begin your Midterm by stating that you have not received outside help on any of these problems. (4 points)

Question 1

The following shows the temperatures (high, low) and weather conditions in a given Sunday for some selected world cities. For the weather conditions, the following notations are used: c = clear; cl = cloudy; sh = showers; pc = partly cloudy.

1. Is “Sampson” an element, variable, or observation?
2. Provide the complete observation for Orderly.
3. Give an example of a quantitative variable from the above table.
4. Provide the range for the low temperatures.
5. Explain why condition is NOT an ordinal variable.

Question 2

A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are shown below.

1. Develop a frequency distribution table for her grades. Remember that tables need titles…
2. From the frequency distribution table, develop an appropriated titled and labeled bar chart for her grades.
3. Construct a pie chart for her grades with five categories of grades. Make sure title and labels are appropriate.
4. All the courses are three credits except for the two that are highlighted. They are science courses and are worth 5 credits each. Using a weighted mean, calculate the student’s grade point average. A = 4.0; B= 3.0; C= 2.0; D =1.0; F = 0

Question 3

The number of hours worked per week for a sample of nine students is shown below.

1. Determine the mean, median, and mode.
2. Explain which of the three values (mean, median, mode) is the best representation of central tendency for this specific problem. Do not give a general answer about what the mean, median, or mode is. The question is designed to see if you can pick which one of these measures of central tendency fits the data the best.
3. What is the standard deviation for the number of hours worked? Does the standard deviation support that the data is clumped together or spread apart? Justify your answer, and make sure the range is mentioned in this justification.

Question 4 – show your work in 1-3.

You are given the following information on Events A, B, C, and D.

P(A) = .3

P(B) = .4

P (C) = 0.61

P(A ∩ B) = 0.1

1. Compute P(A | B).
2. Compute P(A U B)
3. Compute the probability of the complement of B.
4. Are events A and B mutually exclusive? Justify your answer.
5. In P (A │B), which event, A or B, occurred first?

Question 5

When a particular machine is functioning properly, 80% of the items produced are non-defective.

1. If nine items are examined, what is the probability that exactly four are non-defective?
2. If nine items are examined, what is the probability that exactly three are defective?
3. If nine items are examined, what is the probability that at least six are non-defective?
4. If nine items are examined, what is the probability that more than seven are non-defective?

Question 6 – Show your work.

The average starting salary of this year’s graduates of a large university (LU) is $62,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed.

1. What is the probability that a randomly selected LU graduate will have a starting salary of at least $70,000?
2. Individuals with starting salaries of less than $49,000 receive a free class. What percentage of the graduates will receive the free class?
3. What percent of graduates will have their salaries one standard deviation from the mean?
4. What is the range of salaries that are one standard deviation from the mean?

Question 7 – Show work.

A simple random sample of computer programmers in Houston, Texas revealed the sex of the programmers and the following information about their weekly incomes.

1. If all the salaries were written on separate pieces of paper, and one was drawn at random, what is the probability that the one that was drawn would be over $650?
2. If a programmer were selected at random to complete a project, what would the probability be that the programmer was male given that the weekly salary is over $725?
3. If all the programmers’ names were written on separate pieces of paper, what is the probability that two female programmers names were drawn in a row? Assume the first name was not returned to the pile.
4. What is the probability of selecting a female programmer with a weekly salary over $975?

Question 8 – Show work for 1-2.

Students of a small university who eat lunch on campus spend an average of $6.50 a day at their cafeteria. The standard deviation of the expenditure is $0.75. The data is normally distributed.

1. What is the z score of Frank who spent $4.75?
2. What probability corresponds with Frank’s z score?
3. Why was Frank’s z score negative? Why wasn’t his probability negative?
4. Doria spent $9.00 on her lunch on Friday. Explain to her, in terms of standard deviation, why this is not a typical expenditure at this campus.
5. Explain where Doria’s z score falls on the normal distribution curve.