stats 108

Midterm 1 Sample NOTE: Must show all work for credit!

1) Under ________ statistics, we study decision making about population based on sample results.

2) __________ data are data collected on different elements for the same period of time.

3) Indicate whether the following variables are quantitative and which are qualitative. If the variable is qualitative circle only ‘A’ . If the variable is quantitative circle ‘B’. In addition, if the variable is quantitative then also circle ‘C’ for continuous or ‘D’ for discrete in addition to circling ‘B’ for that variable.

Qualitative Quantitative Continuous Discrete 3a) number of cars owned per family A | B C D 3b) brand of a computer A | B C D 3c) width of a person’s foot A | B C D 3d) marital status of people A | B C D 3e) SAT score A | B C D

4) Two households are randomly selected and it is observed whether or not the household has a telephone answering machine. The event “at least one of them owns a telephone answering machine” is an example of a ___________ event?

5) What is the name of the curve drawn for the cumulative frequency distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes? _____________

6) Answer the following questions using the following graph of a variable X (also called C2).

9.68.06.44.83.21.60.0

250

200

150

100

50

0

C2

F re

q u

e n

c y

Histogram of X

6a) Based on the discussions in class and in the book, what type of distribution shape is X?_ _________

6b) Which one is the lowest value, the mode, the mean or the median for variable X? ___________

6c) What approximately is the mode for X? __________ 6d) If the first quartile is 8.51 and the third quartile is 9.69, below what value would be considered an outlier?________

7) Use the following scores for a mathematics class of students for 5 equal intervals 18, 24, 65, 80, 90, 72, 89, 53, 77, 52, 95, 99, 95, 82, 100, 60, 83, 44, 63, 85

Fill out the following table: Score Interval frequency Relative

frequency Cumulative frequency

Cumulative Relative Frequency

[0,20) [20,40) [40, 60) [60, 80) [80, 100]

Go to 3 decimal places on the exam

8) For the following data: 9, 3, 5, 11, -1, 7, 1, 7 8a) What is the sample variance of the data?____

8b) What is the sample standard deviation of the data?_______

8c) What is the mean?

8d) What is the median?

8e) What is the mode? 8f) What is Q1?

8g) What is Q3?

8h) What is the range?

9) If the times of a race, X, follow a normal distribution with mean time of μ=20 seconds and σ2 = 16 seconds squared,

9a) Find the probability of a having a race more than 32 seconds, P(X>32)=

9b) Find the probability of having a race between 12 and 28 seconds, P(12 < X < 28)= P(12<x<28)=0.95

9c) Find P(X<8) + P(X>24)=

10) Roll a die once so that the sample space is S={1,2,3,4,5,6}. Let A be the event of getting an even number. Let B be the event of rolling a number at least 4. B={4,5,6}

10a) P( B ) = ________ 10b) P(A U B) = ________ 10c) P(A ∩ B)= _______

11) The following table lists probability distribution of the number of refrigerators owned by all families in a city. If P(X=0)=P(X=3)=p, what is p?____

X P(X)

0 p 1 .65 2 .27 3 p

12) The following table gives a two–way classification of all employees of a company based on “whether or not they are smokers” and “whether or not they suffer from any allergies.”

Suffers from allergies Yes No

Smoker 35 25 Nonsmoker 55 185

90 210 12a) Given that a person does not suffer from allergies, what is the probability that they are a nonsmoker?__ __

12b) Are “suffer from allergies” and “smokers” independent, why or why not?

13c) What is P(Smoker)=?________

14) If A and B are independent and P(A) = 0.3 and P(B) = 0.5, what is P(A U B)? _________

15) How many ways can we pick 3 contestants for a game show from a group of 10 people?________

16) How many ways can we choose a president and vice president from a group of 6 people?_____

17) If there are 3 choices for lunch and 2 choices for dinner, how many total outcomes can a person choose lunch and dinner?______ 18) If P(A) = 0.5 and P(B) =0.3 and P(A∩B) = 0.1, what is the probability of A or B or both?______ 19) The probability that A occurs, given that B has occured, is 0.35. If the probability that event B occurs is 0.4, what is P(A∩B)?____