1. A company produces an 80-ounce bag of carrots and the weight of a bag of carrots is normally
distributed with mean 80 ounces with standard deviation 4.5 ounces.
(a) What is the probability that a randomly selected bag of carrots will weigh less than 72 ounces?
(b) It turns out that their bags of carrots vary so much in weight and people complained. The
company wants to reduce their standard deviation. What is the appropriate standard deviation if the
company wants 99.6% of their bags weighing between 78 ounces and 82 ounces?
=====================================================================================
2. The FDA granted an “emergency use authorization” for Remdesivir. A study was conducted
investigate the frequency of side effects. The study used 57 coronavirus patients: 35 people received
Remdesivir and 22 people received a placebo. It was found that 20 people taking Remdesivir dropped
out of the study due to side effects compared to 5 people on placebo.
Conduct a test at a 5% level of significance to determine if there is a significant difference between
Remdesivir and placebo in the frequency of side effects. Show all 5 steps properly.
=====================================================================================
3. Amy purchased 3 face masks; one mask from each of 3 different online sites (A, B, C). She paid
for next day shipping on each site. The probabilities of arriving the next day for these sites are 0.92, 0.88,
and 0.96, respectively, and they are independent from sites to sites.
What is the probability that only one of them arrives the next day?
=====================================================================================
=====================================================================================
4. Three students, Abby (A), Diana (D), and Matt (M), are taking a seminar class. Each student is going to
present a topic and the order of presentation will be determined randomly.
(a) List the outcomes (i.e. order of presentation) in the sample space.
(b) What is the probability that one of the women will present first?
(c) What is the probability that Abby will present before Matt does?
=====================================================================================
6. A fast food restaurant employee claims that they serve 85 customers on average during lunch
hour (12:00-1:00 pm). The manager thinks that the employee is exaggerating.
The manager randomly sampled 30 lunch hours to conduct a test. The average number of customers
served was found to be 82.2 with standard deviation 5.8. Conduct a test at the 5% significance level to
determine if the employee is exaggerating or not. Make sure to show all 5 steps.
=====================================================================================
7. A sample of adults were tested to see how far away they could first hear an ambulance coming
towards them. The regression equation between distance (in feet) and age (in years) is given below.
= 600 − 3.2
(a) What is the response variable in the study?
(b) Interpret the slope of the regression line in the context of the problem.
(c) Ben is 40 years old and could hear an ambulance coming towards him when it is 480 feet away.
Can he hear the ambulance from farther away than people his age? Show your work.
=====================================================================================
8. When a law firm represents a group of people in a class action lawsuit and wins that lawsuit, the firm
receives a percentage of the group’s settlement money.
The firm is trying to decide whether to represent car owners in a class action lawsuit against a
manufacturer for a particular defect (certain make and model cars). If less than 5% of the cars have the
defect, the firm will not recover its expenses and lose money. Therefore, the firm will take the lawsuit
only if it is convinced that more than 5% of the cars of this make and model have the defect.
The firm plans to sample 1,000 car owners (this make and model) and ask them if they experienced this
defect. If more than 7% of the sampled car owners experienced this defect, the firm will take the case.
(a) Describe the population of interest.
(b) Describe the main outcome variable of interest.
(c) Describe the parameter of interest in words and state the hypotheses (null and alternative) the
law firm should test using the parameter.
(d) Describe the type I error in the context of the problem.
(e) Describe the potential consequences of committing a type I error.
(f) Calculate the probability of making a type I error.
(g) Suppose that 5.5% of the cars of this make and model actually have the defect. Calculate the
power of the test that the law firm will perform.
=====================================================================================
11. Consider two most-watched TV shows on Netflix: “The Walking Dead” and “Money Heist.” Suppose
that 68% of Netflix subscribers watched The Walking Dead, 46% of Netflix subscribers watched Money
Heist, and 10% of Netflix subscribers watched neither of them.
(a) Find the probability that a randomly selected Netflix subscriber watched both of them.
(b) Among the Netflix subscribers who watched The Walking Dead, what percent did not watch
Money Heist?
=====================================================================================
12. For the following data sets, which one is likely to have a larger variance? Explain why.
• Data Set 1: blood pressure measurement for a person taken daily for 30 days
• Data Set 2: blood pressure measurements for 30 different people
=====================================================================================
0 comments