A snack food company produces 454 g pretzel bags. Although the weight can vary slightly from one bag to another, the company claims that average weight of the pretzel bags is 454 g. In a quality control process, the company would like to test if the true mean bag weight is indeed what they think it is (i.e. test if the true mean is indeed 454 g). They have taken a random sample of 36 bags of this size and weighed them. Suppose that the test statistic came out to be 1.23. What is the p value for the test?   

Character as Social Critique – Choose one major character from The Importance of Being Earnest and explain how Wilde uses that character to critique Victorian society.In your response, analyze how the character reflects or exaggerates social values and explain the broader message Wilde communicates through them. 

Store manager of a retail store collects information about people who use the store’s mobile app to find discounts while they are shopping. Based on his survey, a 90% confidence interval for the true proportion of customers who use the app while they are shopping is from 0.54 to 0.58. What is the 90% confidence interval for the true proportion of those who DO NOT use the mobile app to find discounts while they are shopping.

The housing department of a large city monitors the rent for rent-controlled apartments in the city.  Suppose the rent of a rent-controlled apartment follows a normal distribution with a mean of $2750 and a standard deviation of $650. Find the 75th percentile for the rent-controlled apartments in this city. [fill1] If a rent-controlled apartment is selected at random, what is the probability that the rent of that apartment will be less than $2000? [fill2] If we randomly select 25 rent-controlled apartments, what is the standard error of the sample average? [fill3] If we randomly select 25 rent-controlled apartments, what is the probability the average rent will be less than $2000? [fill4]

The demand for a certain book in a bookstore on any given day is given by the following table, where Y represent the number of purchases of the book on any given day. y 0 1 2 3 4 5 6 7 P(Y=y) 0.10 0.23 0.31 0.12 0.10 0.05 0.05 0.04 On a given day, what is the probability that more than 4 books will be sold? 

Please note that this question consists of three parts. You need to show all mathematical calculations/explanations to get the final answer. Just giving the answer without showing work may result in zero for the question.  Every year at the JSM expo, Penn State has a booth to promote the programs offered by the statistics department. Suppose that the person in charge of the booth always has the following set of free promotional items on the table for the people to pick from:   10 grocery bags 8 lunch bags 15 pens  Suppose that when needed, the items are restored before next person approaches the desk, so each person picks up from this set. Assuming a person is only allowed to pick one item, what is the chance that person picks a lunch bag?  Assuming a person is only allowed to pick one item, what is the chance that person picks either a grocery bag or a lunch bag? If a person is allowed to pick two items, what is the probability that person picks two lunch bags.     

Two studies were conducted to compare the experiences of low-income families receiving food stamps to those receiving cash subsidies.  Study 1: Interviewed 50 families who have been in the food stamps program and 50 families who have received cash subsidies for at least 2 years Study 2: Randomly assigns 50 families to each program and interviews them after two years.   Which of the below statement is correct about these studies? 

A student’s test scores are 88, `b` and `a`.  What grade do they need to get on their fourth test to have a 90 for their final grade? POST YOUR SOLUTION IN THE BOX BELOW.

You want to help Dr. Burnsed get more exercise while she’s working, so you and your classmates suggest an under desk bike (Figure 1 A) so that she can exercise while Yellowdigging. In the model, point b is the pedal where the ball of the foot connects and point p is where the pedal connects to the crank. Between b & p is the distance between the ball of the foot and the pedal. Treat each segment as a rigid body with no mass. Your leg exerts 20C.D N (at point b) in the -x direction on the ball of the foot, calculate the y-direction force at (b) and the x- and y- direction forces at (p). Also determine the magnitude of force on the ball of the foot. The length bp is 9.A inches and is 50.B degrees from the horizontal. Where ABCD are the last 4 digits of your ASU ID.   

What do we mean by a normal distribution?  Give an example of two variables (not included in another question here in the test) that you would expect to be normally distributed.  Enter your answer in the box below.