1.North Carolina State University posts the grade distributions for its courses online. Students in Statistics 101 in the Fall 2007 semester received 26% A's, 42% B's, 20% C's, 10% D's, and 2% F's. Choose a Statistics 101 student at random. To "choose at random" means to give every student the same chance to be chosen. The student's grade on a four-point scale (with A = 4) is a discrete random variable X with this probability distribution:

 

(a) What values of random variable X are represented by the event "the student got a grade better than D"? Write your answer as a comma-separated list. 

(b) What is the probability of the event from part (a)?
 

2.Generate two random numbers between 0 and 1 and take X to be their sum. The sum X can take any value between 0 and 2. The density curve of X is the triangle shown in Figure 10.7 (p. 275) of the 6th edition of Moore, Notz and Fligner.

(a) What is the probability that X is less than 1.6? 
(b) What is the probability that X is less than 0.3?

3.

Let the random variableXbe the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. The distribution for the units is given below.

(a) Is X a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS) 
ANSWER: 

(b) What must be the probability of choosing a unit with 10 rooms? P(X=10) = 

(c) What is the probability that a unit chosen at random is not a 10-room unit? P(X≠10) = 

(d) What is the probability that a unit chosen at random has less than five rooms? P(X<5) = 

(e) What is the probability that a unit chosen at random has between four and six rooms? P(4≤X≤6) = 

 

4.

Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm's public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness, the choice will be made by drawing two names from a hat. (This is an SRS of size 2.)

(a) Write down all possible choices of two of the five names. This the sample space. Note: Please input, for example, (Abby, Mei-Ling) or (A, M) to include a pair and use comma AND a space to separate each pair. 
(b) The random drawing makes all choices equally likely. What is the probability of each choice?
(c) What is the probability that Deborah is chosen?
(d) What is the probability that neither Abby nor Sam is chosen?

 

5.

The score on an exam from a certain MAT 112 class,X, is normally distributed withμ=76.8andσ=9.4.

 

NOTE: Assume for the sake of this problem that the score is a continuous variable. A score can thus take on any value on the continuum. (In real life, scores are often treated as if they were continuous values but are actually discrete in most cases.)

(a) Write the event ''a score less than 66.8'' in terms of X:  .

(b) Find the probability of this event: 

(c) Find the probability that a randomly chosen score is greater than 83.8:  .

(d) Find the probability that a randomly chosen score is between 66.8 and 83.8: 

 

6.

The Normal distribution with meanμ= 6.8 and standard deviationσ= 1.6 is a good description of the Iowa Test vocabulary scores of seventh grade students in Gary, Indiana. This is a continuous probability model for the score of a randomly chosen student. Figure 3.1 (p. 68) pictures the density curve. Call the score of a randomly chosen student X for short.

Note: If necessary, use <= to represent ≤ and >= to represent ≥.

(a) Write the event "the student chosen has a score of 5.2 or higher" in terms of X. 

(b) Find the probability of an event which represents "the student chosen has a score of 5.2 or higher". 

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