Show your work for credit! If work is needed for a problem and is not there, a significant deduction occurs. 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.City High Low Condition Population in thousands Bad Water 60 12 pc 200 Bigfoot 80 70 pc 750 Mortimer 94 57 sh 500 Orderly 72 50 pc 300 Pierce 44 20 c 45 Sampson 75 52 cl 1501. Is “Condition” an element, variable, or observation? 2. Provide the observation for Pierce. 3. Provide the range for the low temperatures. 4. What type of variable is population? Why?Question 2 A student has completed 12 courses in the School of Arts and Sciences. Her grades in the courses are shown below.D A C FA B F AA A C B1. 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. All the courses are three credits. Using a weighted mean, calculate the student’s grade point average. A = 4.0; B= 3.0; C= 2.0; D =1.0; F = 0Question 3 The number of hours worked per week for a sample of ten students is shown below.Student Hours1 52 393 284 105 166 267 348 369 510 321. Determine the mean, median, and mode. 2. What is the range of the data for the hours worked? 3. What is the standard deviation for the number of hours worked? 4. 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 – Given P(A) = 0.62; P(B) = 0.37; P(A∩B) = 0.061. What is the probability of Event A happening given that Event B already happened? 2. What is the compliment of B? 3. Are Events A and B mutually exclusive? Why or why not? 4. Calculate P(A U B).Question 5 – binomial When a particular machine is functioning properly, 95% of the items produced are non-defective. 1. If 18 items are examined, what is the probability that exactly 15 are non-defective? 2. If 18 items are examined, what is the probability that exactly 2 are defective? 3. If 18 items are examined, what is the probability that at least 14 are non-defective?Question 6 – The average starting salary of this year’s graduates of a large university (LU) is $61,000 with a standard deviation of $3,500. 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 $54,700? 2. Individuals with starting salaries of less than $52,000 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. List a salary that does NOT fall within three standard deviations of 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.Programmer Weekly IncomeA – Female $550B – Male $654C – Female $911D – Male $630E – Female $727F – Female $688G – Male $1000H – Male $8921. 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 $850? 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?Question 8 – Show work for 1-2. Students of a small university who eat lunch on campus spend an average of $4.50 a day at their cafeteria. The standard deviation of the expenditure is $0.70. The data is normally distributed.1. What is the z score of Frank who spent $4.00? 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 $1.75 on her lunch on Friday. Explain to her, in terms of standard deviation, why this is not a typical expenditure at this campus.