Scribd
Upload
25 views1 page

Assignments

The document discusses a local bakery's pastry sales, which are normally distributed with a mean of 120 and a standard deviation of 15. It poses questions regarding the nature of the random variable, the probability of selling exactly 120 pastries, the probability of selling between 100 and 140 pastries, and the sales threshold for the top 10%. Additionally, it addresses the impact of increasing the sample size on the precision of the mean estimate and the confidence interval width, as well as the joint distributions of daily active users and average revenue per user for two mobile games being launched by a game development company.

Uploaded by

Dinker Mattam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
25 views1 page

Assignments

The document discusses a local bakery's pastry sales, which are normally distributed with a mean of 120 and a standard deviation of 15. It poses questions regarding the nature of the random variable, the probability of selling exactly 120 pastries, the probability of selling between 100 and 140 pastries, and the sales threshold for the top 10%. Additionally, it addresses the impact of increasing the sample size on the precision of the mean estimate and the confidence interval width, as well as the joint distributions of daily active users and average revenue per user for two mobile games being launched by a game development company.

Uploaded by

Dinker Mattam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
You are on page 1/ 1

1. A local bakery sells pastries.

From historical data for 30 days, the distribution of daily pastry sales is
known to be normally distributed with a mean (𝜇) of 120 and a standard deviation (𝜎) of 15.
a) What is the random variable here? Is it continuous or discrete? How do you decide? Comment
on the chosen distribution in light of your Based on the given information, how do you say
whether it is continuous or discrete?
b) What is the probability that on a given day, exactly 120 pastries are sold?
c) Calculate the probability that on a given day, between 100 and 140 pastries are sold.
d) If the top 10% of sales days receive a special bonus for the staff, how many pastries must be
sold in a day to reach this top 10%?
e) How would increasing the sample size of days observed from 30 days to 60 days affect the
precision of your estimate for the mean number of pastries sold per day? Specifically discuss
how the standard error of the mean would change if the sample size increases from 30 days to
60 days. How does this affect the width of the confidence interval?

2. Consider a game development company that is launching two new mobile games simultaneously. The

(ARPU) for each game over the first month. The DAU is denoted as 𝑋 for Game A and 𝑌 for Game B.
company decides to monitor both the daily active users (DAU) and the average revenue per user

The ARPU is denoted as 𝑍 for Game A and 𝑊 for Game B. It is observed that the joint distributions of
(𝑋,𝑍) and (𝑌,𝑊) follow a multivariate normal distribution.

You might also like