binomial uniform and normal

Please read the additional materials. Ignore the following below. Thank you. BUS 190HW 9 – Random variables, binomial, uniform, normal AS USUAL- SHOW YOUR WORK- SHOW GRAPHS WHERE APPROPRIATE General random variable Suppose you have a box of 10 tickets, with 3 green tickets and 7 yellow tickets. If you pick a green ticket out of the box, you get $10. If you pick a yellow ticket, you have to pay $5.Let the random variable X be the amount you get (if you have to pay, it is negative ‘pay’) after 1 draw from this box. Set up the table for this random variable X, and indicate why it is a good random variable table (hint: check valid probability for each value of X and they sum to 1).
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BUS 190
HW 9 – Random variables, binomial, uniform, normal
AS USUAL – SHOW YOUR WORK- SHOW GRAPHS WHERE APPROPRIATE
1. General random variable
Suppose you have a box of 10 tickets, with 3 green tickets and 7 yellow tickets. If you pick a green
ticket out of the box, you get $10. If you pick a yellow ticket, you have to pay $5. Let the random
variable X be the amount you get (if you have to pay, it is negative ‘pay’) after 1 draw from this box.
a. Set up the table for this random variable X, and indicate why it is a good random variable table
(hint: check valid probability for each value of X and they sum to 1).
b. Calculate E(X)
c. Calculate Var(X)
d.
2. Binomial
Suppose according to past data for a small boutique, about 30% of the customers who walk into
the store purchase at least one item.
a. Today 10 individual customers walked into the store while you are there. How many of these 10
customers do you expect would by at least one item? (hint: expected value formula)
b. What is the chance that exactly 3 of the customers would purchase at least one item?
c. What is the probability that no more than 3 customers would purchase at least one item? (Hint:
sketch a table for the number of people who would purchase at least one item out of the 10.
You do not need to put in all the probabilities, just all the values of X. For which values of X
would you have to add the probabilities? Student who were in my BUS 90 class are familiar with
this problem. Feel free to help your fellows on Canvas discussion this weekend.)
Binomial again
You are in charge of setting up a lunch with 4 of your friends. You have agreed to buy a take-out lunch at
a small café that makes sandwiches. Today’s daily specials are a turkey sandwich and a club sandwich
(but more interesting than our first introduction to LP’s recipe). Suppose they order the type of
sandwich independently, and the chance of ordering a turkey sandwich is 0.6.
a. What is the chance that all 5 of you (you and 4 friends) order turkey sandwiches?
b. What is the chance that NONE of the 5 of you order turkey sandwiches?
c. How many turkey sandwiches would you expect to order (hint: E(X))
d. What is the chance of ordering exactly the expected number of turkey sandwiches?
(you have to solve c first)
e. What is the chance that at least 4 of you order sandwiches?
3. Uniform
A package delivery service breaks up its shipping charges into weight classes, where the package
weights are uniformly distributed WITHIN each weight class.
a. Suppose one of the shipping classes is 12 to 15 lbs. What proportion of packages in this class
would weigh less than 14 lbs?
b. What proportion would weigh more than 12.5 lbs?
c. What would the average weight for a package in this class be?
4. Uniform distribution
The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65
minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74
minutes.
a. What is the probability that the commuting time will be less than 70 minutes? (draw the graph
and shade in the appropriate area!)
b. What is the probability that the commuting time will be between 65 and 70 minutes? (draw the
graph and shade in the appropriate area!)
c. What is the probability that the commuting time will be greater than 65 minutes? (draw the
graph and shade in the appropriate area!)
d. What is the expected (average) commuting time?
5. Uniform again
A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an
approximately uniform distribution between 20 and 40 minutes.
a. What is the probability that the shopping time will be between 25 and 30 minutes? (draw the
graph and shade in the appropriate area!)
b. What is the probability that the shopping time will be less than 35 minutes? (draw the graph and
shade in the appropriate area!)
c. What is the probability that the shopping time will be more than 27 minutes? (draw the graph
and shade in the appropriate area!)
d. What is the mean shopping time?
6. Practice with normal – draw graphs with correct area shaded in and proper x and z axes. Use the
tables I handed out in class. If you do not have such tables, google a set to use. To have tables
similar to those I gave you, go back to the assignment where one is attached.)
The fill amount in 2-liter soft drink bottles is normally distributed with a mean of 2.0 liters and a
mean of 0.05 liters. If bottles contain less than 95% of the listed net content (i.e., less than 1.90
liters) the manufacturer may be subject to penalty by the state office of consumer affairs.
Bottles that have a net content above 2.10 liters may cause excessive spillage upon opening.
What is the probability that a randomly selected bottle will contain:
a. Between 1.90 and 2.00 liters?
b. Between 1.90 and 2.10 liters?
c. Below 1.90 liters or above 2.10 liters?
d. About least how much soft drink (in liters) is contained in 99% of the bottles?
e. 99% of the bottles contain an amount that is between which two values, symmetric about the
average?

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