Question

Textbook prices have a seasonal structure on Ebay. At the end of a term, the supply of used books outstrips demand, and the price is lower. Near the start of a term, many students are looking for books, and the price is higher. Suppose we can classify sales for a particular chemistry textbook into these two time periods and an "other" time period in the proportions shown below. We have also listed the average price the textbook sells for in each of these three time periods
Start-of-term End-of-term Other
Sales proportion 0.45 0.31 0.24
Average price $82.52 $49.12 $65.23
For example, about 45% of Ebay auctions for this chemistry textbook occur at the start of the term and the books sell for an average of $82.52 during this time. Using the information above, compute the average price of the textbook over all seasons. (Do not put a dollar sign in your answer.)
The following is a table of probabilties calculated from a survey of BHCC students with the question asked "How many classes are you taking this semester?"
x: # of classes 1 2 3 4 5
P(x) 0.24 0.26 0.12 0.3 0.08
Using the table, find the following probabilities for a student selected at random:
a.) What is the probability that a student is taking 2 or more classes?
b.) What is the probability that a student is taking at least 3 classes?
c.) What is the probability that a student is taking more than 3 classes?
d.) What is the probability that a student is taking less than 2 classes?
e.) What is the probability that a student is taking no more than 2 clases?
f.) What is the average (mean) amount of classes a student takes at BHCC?
g.) What is the standard deviation for the amount of classes a student takes at BHCC? (round to two decimal places)

Answer 1

Answer:

(1)$68.02

(2)

a.) $P(x\geq 2)=0.76$

b.) $P(x\geq 3)=0.5$

c.) $P(x> 3)=0.38$

d.) $P(x< 2)=0.24$

e.) $P(x\leq 2)=0.5$

f)$\mu=2.72$

g)$\sigma=1.33$

Step-by-step explanation:

Question 1

The probability distribution table for the average price of the textbook sales in each of these three time periods is given below:

$\left|\begin{array}{c|c|c|c}& Start-of-term& End-of-term& Other\\ Sales proportion&0.45&0.31&0.24\\ Average price&\ 82.52&\ 49.12&\ 65.23\end{array}\right|$

We are required to calculate the average price of the textbook over all seasons.

Expected Value

$= (0.45 X 82.52)+(0.31 X 49.12) +(0.24 X 65.23)\\=68.02$

The average price of the textbook over all seasons is $68.02

Question 2

Distribution Table for Number of Courses being taken by BHCC Students

$\left|\begin{array}{c|ccccc}x (No of classes)& 1&2&3 &4&5\\P(x)&0.24&0.26&0.12&0.3 &0.08\end{array}\right|$

a.) Probability that a student is taking 2 or more classes

$P(x\geq 2)=0.26+0.12+0.3+0.08=0.76$

b.) Probability that a student is taking at least 3 classes

$P(x\geq 3)=0.12+0.3+0.08=0.5$

c.) Probability that a student is taking more than 3 classes

$P(x> 3)=0.3+0.08=0.38$

d.) Probability that a student is taking less than 2 classes

$P(x< 2)=0.24$

e.) Probability that a student is taking no more than 2 classes

$P(x\leq 2)=0.24+0.26=0.5$

f)Average (mean) amount of classes

$=(1*0.24)+(2*0.26)+(3*0.12)+(4*0.3)+(5*0.08)\\\mu=2.72$

g)Standard deviation for the amount of classes

$\left|\begin{array}{c|ccccc|c}x (No of classes)& 1&2&3 &4&5&Sum\\x-\mu&-1.72&-0.72&0.28&1.28&2.28\\(x-\mu)^2&2.9584&0.5184&0.0784&1.6384&5.1984\\P(x)&0.24&0.26&0.12&0.3 &0.08\\--&--&---&---&--&--&--\\(x-\mu)^2P(x)&0.71&0.13&0.01&0.49&0.42&1.76\end{array}\right|$

Standard Deviation

$=\sqrt{\sum(x-\mu)^2P(x)} \\=\sqrt{1.76} \\\sigma =1.33$