# Quantitative Methods – MJ8 – 03-30-21 – Sect1

**Module 4/Midterm Homework **

Please complete the following questions. Provide your answers in a different colored font to make them easily identifiable. Each question is worth 1 point. Points are listed for the Excel sheets.

The problems cover information presented in Module 1 through Module 4. Please review documents and videos provided in the learning resources as needed. You will notice the Excel file contains 4 sheets, but the sheets are empty. For this assignment you will need to enter the data into Excel to solve the problems.

**Part 1 (Modules 1 & 2): 17 pts Total**

**Enter the data below into the Module 4 Midterm Homework Excel file on the sheet labeled Part 1. Then use Excel to solve the following problems and record your answer below: Excel sheet should include a minimum of descriptive statistics box and Coefficient of variation box (2 points)**

The number of tickets wrote by police officers in Indianapolis for 35 days: 16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 31, 31, 32, 32

Answer the following questions: **1 point per question**

The mean of the data is? ________

The median of the data is? ________

The first quartile of the data is? ________.

Th third quartile of the data is? ________.

The range of the data is? ________.

The interquartile range of the data is? ________.

The variance of the data is? ________.

The standard deviation of the data is? ________.

The coefficient of variation of the data is ________ percent.

The five-number summary for the data in the sample consists of _______, ________, ________, ________, ________.

Construct a box-and-whisker plot for the data **Box-an-whisker plot: 3 points**

- One point for line at the median and box at correct points
- One point for outer lines at the correct points
- One point for general appearance.

What is the shape of the distribution for the number of tickets written? _______________

Without the box-and-whisker plot what calculations would you use to discuss the shape of the distribution? Provide explanation.

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**Part 2: 13 Points Total**

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**Enter the following data into the spreadsheet labeled Part 2 of the Module 4 Excel file. Then solve the following problem in Excel and answer the questions below. **

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Given below is the amount of milk in gallons produced by a dairy operation for 25 days.

115, 97, 100, 117, 132, 124, 116, 102, 122, 103, 108, 111, 91, 115, 123, 117, 94, 117, 122, 128, 102, 129, 113, 116, 130

Construct a steam-and-leaf diagram for the data set (Module 4). **2 points **

**1-point proper stems****1-point proper leaves**

Construct a frequency distribution, cumulative percentage distribution for the data set. Using the following distribution (Module 3):

90 but less than 100

100 but less than 110

110 but less than 120

120 but less than 130

130 but less than 140 **3 points**

**1 point for correct bins****1 point for correct frequency****1 point for correct cumulative %**

Construct a histogram and cumulative percentage polygon for the defects data, using “90 but less than 100” as the first class (Module 3). **4 points:**

**1 point for histogram****1 point for cumulative percentage****1 point for correct labels on chart****1 point for chart appearance**

Answer the following questions: **1 point per question **

What percentage of days did the dairy operation produce 120 but less than 130 gallons of milk? ________

What percentage of days did the dairy operation produce less than 120 gallons of milk? _________

What percentage of days did the dairy operation produce at least 100 gallons of milk? ______

What percentage of days did the dairy operation produce at least 100 gallons but less than 130 gallons of milk? _________

**Part 3: 10 points total**

**On sheet 3 of your excel file, complete the contingency grid with the provided information and then answer the questions. (Hint: Remember to use the probability worksheet from Module 3): **

**Contingency grid 3 points: **

**1 point for titles/labels****1 point for data****1 point for totals.**

Suppose that patrons of a restaurant were asked whether they preferred water or whether they

preferred soda. 70% said that they preferred water. 60% of the patrons were male. 80% of the males preferred water.

Answer the following questions: **1 point per question **

The probability a randomly selected patron prefers soda is __________.

The probability a randomly selected patron is a female is __________.

The probability a randomly selected patron is a female who prefers soda is __________.

The probability a randomly selected patron is a female who prefers water is __________.

Suppose a randomly selected patron prefers soda. Then the probability the patron is a male is _________.

Suppose a randomly selected patron prefers water. Then the probability the patron is a male is ________.

Suppose a randomly selected patron is a female. Then the probability the patron prefers water is _______.

**Part 4: 10 points total**

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**Given the following scenario answer the following questions using the functions in your Excel file on sheet 4. Include the question number in column A then the equation in Column B. Include all calculations completed outside of excel below with the answers. Make sure Answers are easy to find (Module 4). **

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Answer the following questions: **1 point per question **

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A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels.

Find the probability all the hotels in the sample offered hairdryers in the bathrooms. __________

Find the probability that more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms. __________

Find the probability that at least 9 of the hotels in the sample **do not **offer hairdryers in the bathrooms. _______

The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day.

Find the probability that less than 6 tickets are written on a randomly selected day from this population. __________

Find the probability that exactly 6 tickets are written on a randomly selected day from this population. ___________

You were told that the scores on a statistics exam were normally distributed with a mean score of 75 and a standard deviation of 15.

What is the probability of a score greater than 95? _________

What is the probability of a score lower than 55? __________

What is the probability of a score between 75 and 90? ______

What is the probability of a score between 60 and 75? ______

What is the probability of a score between 60 and 95? ______