# Week 4 Weather Conditions Element Variable or Observation Midterm

# Midterm

**There are 8 questions in total, each worth 12.5 points. Please upload your answers to the dropbox. The Grantham Late policy applies to the midterm, and it is a 5% deduction per late day. Remember that work is required. That work may be calculations, a computer printout, an Excel program – but there has to be something that shows where numbers came from. This midterm may only be taken one time.**

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.

- Is “condition” an element, variable, or observation?
- Provide the observation for Mexico City.
- Give an example of a quantitative variable.
- Provide the range for the low temperature.
- What is the mode for the high temperature?
- Explain why the “lo” is not ordinal.

Question 2

A student has completed 16 courses in the School of Arts and Sciences. Her grades in the 16 courses are shown below.

D |
D |
C |
D |

A |
B |
F |
A |

A |
A |
C |
B |

B |
C |
C |
D |

- Develop a frequency distribution table for her grades.
- Create a bar chart for her grades. Remember the importance of good titles and labeled axes.
- 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 ten students is shown below.

Student |
Hours |

1 |
33 |

2 |
40 |

3 |
15 |

4 |
25 |

5 |
15 |

6 |
30 |

7 |
32 |

8 |
10 |

9 |
15 |

10 |
35 |

- Determine the mean, median, and mode.
- Explain which of the three values (mean, median, mode) is the best representation of central tendency in this particular set of data. (This is not an “in general” question.)
- What is the standard deviation for the number of hours worked? What does standard deviation tell us?
- Create a histogram for this data. Discuss whether or not this data is normally distributed. Justify your answer.

Question 4

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

P(A) = .5

P(B) = .3

P (C) = .20

P(A U D) = .8

P(A ∩ C) = 0.05

P (A │B) = 0.22

P (A ∩ D) = 0.25

- Compute P(D).
- Compute P(A ∩ B).
- Compute P(A | C).
- Compute the probability of the complement of C.
- What does it mean to be mutually exclusive? Give an example.

Question 5

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

- If seven items are examined, what is the probability that three are defective?
- If seven items are examined, what is the probability at at least three are non-defective?
- If seven items are examined, what is the probability that at most, one is defective?
- What is the expected number of defective items if ten items are examined?

Question 6

The average starting salary of this year’s graduates of a large university (LU) is $34,000 with a standard deviation of $7,000. Furthermore, it is known that the starting salaries are normally distributed.

- What is the probability that a randomly selected LU graduate will have a starting salary of at least $32,000?
- Individuals with starting salaries of less than $19,900 receive a low income tax break. What percentage of the graduates will receive the tax break?
- What percent of graduates will have their salaries one standard deviation from the mean?
- What is the range of salaries that is one standard deviation from the mean?
- What is the range of salaries that are two standard deviations from the mean?

Question 7

A simple random sample of 8 computer programmers revealed the sex of the programmers and the following information about their weekly incomes.

Programmer |
Weekly Income |
Sex |

A |
$550 |
M |

B |
$654 |
M |

C |
$911 |
F |

D |
$500 |
M |

E |
$727 |
M |

F |
$688 |
F |

G |
$1000 |
F |

H |
$892 |
M |

- 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 $700?
- If a programmer were selected at random to complete a project, what would the probability be that the programmer was male?
- What is the probability of selecting an income of under $700 per week given that a male was selected?
- If all the salaries with the name of who earned it were written on separate pieces of paper and two were drawn at random (the first one was NOT returned to the pile), what is the probability that both were female?
- If all the salaries with the name of who earned it were written on separate pieces of paper and two were drawn at random (the first one was NOT returned to the pile), what is the probability that the first draw would be the salary of a male and the second would be one of a female?

Question 8

Students of a large university spend an average of $7 a day on lunch. The standard deviation of the expenditure is $2. A simple random sample of 25 students is taken.

- What is the probability that the sample mean will be at least $4?
- Jason spent $15 on his lunch. Explain, in terms of standard deviation, why his expenditure is not usual.
- Explain what information is given on a z table. For example, if a student calculated a z value of 2.77, what is the four-digit number on the z table that corresponds with that value? What exactly is that 4-digit number telling us?
- Explain why we use z formulas. Why don’t we just leave the data alone? Why do we convert?

Grading Criteria Assignments |
Maximum Points |

Meets or exceeds established assignment criteria | 40 |

Demonstrates an understanding of lesson concepts | 20 |

Clearly presents well-reasoned ideas and concepts | 30 |

Uses proper mechanics, punctuation, sentence structure, and spelling | 10 |

Total |
100 |