Chapter 6 to 8 Supplemental Homework

1.  Hadey the goat and Taylor the tailor are preparing to launch their new clothing line collab “Commes des Mouflons”. The preorders
for the jackets are already rolling in, with the number of orders each day “X” having the distribution shown below. Assume that
the number of orders each day is an independent variable.

a. Describe the shape of the distribution of daily jacket orders.
b. How many jacket orders should Taylor and Hadey EXPECT each day?
c. What is the standard deviation of the number of daily jacket orders?
d. How many jacket orders should Taylor and Hadey EXPECT each week?
e. What is the standard deviation in the TOTAL number of jacket orders per WEEK?

f. If the pre-order price for a jacket is $240, how much revenue should Hadey and Taylor EXPECT in the month of May?
g. If each jacket takes Taylor 3 hours to produce, how much time should she EXPECT to devote to production for the
month of May?
h. What is the standard ERROR in the number of jacket orders per day in the month of May?
i. What shape does the distribution of the mean orders PER DAY in the month of May look like?
j. Taylor doesn’t want to give up her existing business, so she’s looking to hire an assistant to help with the jackets. Hadey
says that they can’t afford that unless they bring in more than $4000 from pre-orders in May. Recall that the
pre-order price is $240 per jacket. How many TOTAL pre-orders would they need in May to meet this goal?
k. In order to meet the number of orders you found in part j, how many jacket pre-orders would need to come in PER DAY
in the month of May?
l. Using your calculations from parts j and k, what is the probability that Hadey and Taylor will get enough jacket
pre-orders in the month of May to afford to hire an assistant?

2.   Hadey is planning a campaign to secure voting rights for the goats of Avocado Park. At the moment, 53% of the residents who are
eligible to vote support the idea, but Hadey doesn’t know that. He wants to assess the popular mood, so he selects a random sample
of 47 eligible voters from the neighborhood and asks them if they support votes for goats.

a. If you wish to use the binomial distribution to model the number of members of this sample that will support votes
for goats, what must you first assume? Be precise.
b. What is the probability that exactly 20 members of his sample support votes for goats?
c. What is the probability that more than HALF of the members of his sample support votes for goats?
d. How many members of his sample would you EXPECT to support votes for goats?
e. What is the standard deviation of the number of members in a sample of this size that support votes for goats?
f. Describe the shape of the distribution of the variable “p-hat” representing the proportion of members of each
possible sample of size 43 that supports votes for goats. g. What are the mean and standard deviation of the variable
“p-hat” described in part f?

3.   As part of his market research, Hadey has sampled 42 random residents of Avocado Park and asked them how much they would
be willing to pay for a Commes des Mouflons jacket. The results can be found in the file “Commes des Mouflons.xlsx” on Canvas.
a. Are there any outliers in the data set? Explain, but do not remove any that you find.
b. Is it plausible that this data set could have come from a normally distributed population? Explain.
c. Can we reasonably claim that the distribution of the mean prices offered by members of all samples of 42 Avocado
Park residents for a Commes des Mouflons jacket is normal? Why or why not?

4.   Suppose that the time it takes Taylor to make one of the Commes des Mouflons jackets is in fact variable and uniformly distributed
between 2.25 and 3.5 hours for each jacket.
a. Draw a graph of the distribution of “T”, the amount of time it takes Taylor to make a jacket. Make sure to notate the
density!
b. What is the probability that it will take Taylor LESS than 3 hours to make the next jacket?
c. What is the probability that it will take Taylor MORE than 2.5 hours to make the next jacket?
d. What is the probability that it will take Taylor EXACTLY 3 hours to make the next jacket?
e. How long should Taylor EXPECT to take to make the next jacket?
f. What is the standard deviation of the variable “T”?
g. Suppose that in May and June combined Commes des Mouflons receives 37 orders for jackets. Taylor estimates
that she can spare a total of 100 hours to make these jackets without it cutting into her other business. How many
hours can she spare for EACH jacket?
h. Describe the distribution of the EXPECTED number of hours Taylor will need to spend making EACH of the 37
jackets ordered in May and June. Include the mean, standard deviation AND the shape of the distribution.
i. Using your calculations from parts g and h, what is the probability that Taylor will be able to finish the 37 jackets
without it cutting into her other business?