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ASU Enrollment Summary. According to the Arizona State University Enrollment Summary, a frequency distribution for the number of undergraduate students attending Arizona State University ( ASU ) in the Fall 2012 semester, by class level, is as shown in the following table. Here , 1 = freshman , 2 = sophomore , 3 = junior , and 4 = senior.

Class level
1234
No. of students
9,652
11,115
17,302
21,114

Let X denote the class level of a randomly selected ASU undergraduate.

(a) What are the possible values of the random variable X?

(b) Use random-variable notation to represent the event that the student selected is a junior ( class - level 3 ).

(c) Determine P ( X = 3 ), and interpret your answer in terms of percentages.

(d) Determine the probability distribution of the random variable X.

(e) Construct a probability histogram for the random variable X.

Short Answer

Expert verified

Part (a) 1, 2, 3, and 4.

Part (b)X=3

Part (c) 0.2923

Part (d)

X1234
P(X)0.16310.18780.29230.3568

Part (e)

Step by step solution

01

Part (a) Step 1. Given information.

The following table shows the frequency distribution of undergraduate students attending Arizona State University (ASU) in the Fall 2012 semester by class level.

1 indicates a freshman, 2 indicates a sophomore, 3 indicates a junior, and 4 indicates a senior.

Class level
1234
No. of students
9,652
11,115
17,302
21,114
02

Part (a) Step 2. Find the possible values of X.

We can observe from the given table that for a random variable X the possible values are 1, 2, 3, and 4.

03

Part (b) Step 1. If the student chosen is a junior, use random-variable notation to represent it.

Here the value of x becomes 3.

The notation is X=3.It represents the event that the selected student is from a junior class of level 3.

04

Part (c) Step 1. Find P(X=3). 

Here 3 represents the junior which includes 17,302 students.

P(X=3)=fN=17,30259,183=0.2923
05

Part (d) Step 1. Find the probability distribution of the random variable X.

XPX=x
19,65259,183=0.1631
211,11559,183=0.1878
317,30259,183=0.2923
421,11459,183=0.3568
06

Part (e) Step 1. Draw a probability histogram for X. 

To make a probability histogram, use MINITAB.

Procedure for MINITAB:

Step 1: Select Graph>Bar Chart from the drop-down menu.

Step 2: Select Values from a table from the Bars indicate section.

Step 3: Select Simple under One column of values. Click OK

Step 4: In Graph variables, type P (X = x) in the column.

Step 5: Fill in the X column in the Categorical variable.

Step 6: Click the OK button.

Step 7: Go to the Scale tab and select the horizontal axis.

Step 8: Type 0 in the Gap between clusters field.

Step 9: Click the OK button.

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