Question

In: Statistics and Probability

Suppose my grocery store of choice has 20 shopping carts in total and 10 of them...

Suppose my grocery store of choice has 20 shopping carts in total and 10 of them have wobbly wheels (they don’t really push properly). I’ve gone to the store with 3 of my friends to stock up for a big party and we decide to split up (each of us taking a cart, so 4 carts in total). Let X be the number of carts with wobbly wheels (out of the 4 me and my friends have taken).What is the distribution of X?Give the name of the distribution and the appropriate parameters.What is the mean and variance of this distribution? Give your answer as a number,but include the formulas (or logic) used.

What is the probability exactly 2 of us have carts with wobbly wheels?

What is the probability that at least 1 of us has a cart with wobbly wheels?

Expert Solution

Here X denotes the number of carts with wobbly wheels out of the 4 taken. The distribution of X is binomial distribution as it follows the following requirements for a binomial distribution.

1) There must be n independent and identical trials.

2) There is a non-zero constant probability of success.

3) There must be two outcomes for the variable.

Here the possible two outcomes of X are cart with wobbly wheels (assumed as success), and cart without wobbly wheels (assumed as failure). The selection of the carts are independent to each other and random. The probablity of getting cart with wobbly wheels is 10 / 20 = 0.5. So X has a binomial distribution with parameters n = 4 and p = 0.5. The probability distribution for X is given as

for x = 0, 1, 2, 3 and 4.

The mean of the distribution is given as np = 4(0.5) = 2

The variance of the distribution is given as np(1-p) = 4(0.5)(0.5) = 1

The probability that exactly 2 of us have carts with wobbly wheels is given as .

The probability exactly 2 get the wobbly wheels is 0.375.

The probability that at least 1 of 4 has a cart with wobbly wheels is given as

The probability that at least 1 of 4 has a cart with wobbly wheels is 0.9375.

orchestra answered 2 years ago

While going to the grocery store it's not unusual to find stray shopping carts littering the...

While going to the grocery store it's not unusual to find stray shopping carts littering the parking lot. Shoppers may think that a parking spot is open, only to find that it's actually being used by a shopping cart. It seems like a basic courtesy to others: you get a cart at the grocery store, you use it to get your groceries and bring them to your vehicle, and then you return it for others to use. And yet, it's...

Think of shopping at a grocery store. Describe how the model of consumer choice would explain...

Think of shopping at a grocery store. Describe how the model of consumer choice would explain your decision-making process while shopping at a grocery store. You must use the concepts of budget constraint, marginal utility, and marginal utility per dollar in your description. Feel free to choose products you might buy at the grocery store and create marginal utilities over the quantities of these products (if you wish to get detailed). 1-3 paragraph answers, please, and don't copy from other...

draw traceability matrix for online shopping system ( online grocery store)

A woman was shopping in the deli department of a grocery store. She slipped and fell...

A woman was shopping in the deli department of a grocery store. She slipped and fell on some grease on the floor from the rotisserie chickens. The woman went to the emergency room and established that she had a broken wrist. The woman sued the grocery store for negligence. List the four elements required to establish the tort of negligence in this case. Then, relate each element you have listed to this case. Write your answer using the format below:...

Bryce is at the local grocery store, shopping for himself and his girlfriend Renee. This week,...

Bryce is at the local grocery store, shopping for himself and his girlfriend Renee. This week, chicken breasts are on sale for 45 percent off the regular price. What two effects does Bryce face that may cause him to purchase more chicken breasts this week than he did last week?

Larry is at the local grocery store, shopping for himself and his friends, Moe and Curly....

Larry is at the local grocery store, shopping for himself and his friends, Moe and Curly. This week, ground hamburger is on sale for 35 percent off the regular price. How does the sale impact his budget constraint compared to all other goods? Explain the two effects Larry faces that may cause him to purchase more ground hamburger this week than he did last week?

. You are holding a shopping basket at the grocery store with two 0.62-kg cartons of...

. You are holding a shopping basket at the grocery store with two 0.62-kg cartons of cereal at the left end of the basket. The basket is 0.61 m long. Where should you place a 1.9-kg half gallon of milk, relative to the left end of the basket, so that the center of mass of your groceries is at the center of the basket?

You are holding a shopping basket at the grocery store with a 1.24-kg carton of cereal...

You are holding a shopping basket at the grocery store with a 1.24-kg carton of cereal at the left end of the basket. The basket is 0.61 m long. Where should you place a 1.9-kg gallon of milk, relative to the left end of the basket, so that the center of mass of your groceries is at the center of the basket? Hello ! I'm studying for a test tomorrow and looking for steps on how to do this.

Create a Python 3 program that acts as a grocery store shopping cart. 1. Create a...

Create a Python 3 program that acts as a grocery store shopping cart. 1. Create a class named GroceryItem. This class should contain: - an __init__ method that initializes the item’s name and price - a get_name method that returns the item’s name - a get_price method that returns the item’s price - a __str__ method that returns a string representation of that GroceryItem - an unimplemented method is_perishable Save this class in GroceryItem.py. 2. Create a subclass Perishable that...

Imagine you work for an independent grocery store with 20 employees. The business owner has tasked...

Imagine you work for an independent grocery store with 20 employees. The business owner has tasked you with creating a relational database that will track employee names, IDs, positions (e.g., cashier, manager, clerk, or night crew), and salaries. Create a relational database table in Microsoft® Access® or MySQL® for the grocery store using the attached data points. Apply the universal rules (unique primary keys, unique column names, no duplicate rows) to your table. Include all necessary null values. Display in...