A survey was conducted in which 125 families were asked how many cats lived in their households. The results are shown below. ​a) What is the probability that a randomly selected family has one​ cat? ​b) What is the probability that a randomly selected family has more than one​ cat? ​c) What is the probability that a randomly selected family has​ cats? ​d) Is this an example of​ classical, empirical, or subjective​ probability? *Number of Cats-Number of Households* 0-71 1-33 2-16 3-4 4-1 Total-125 ​a) The probability that a randomly selected household has one cat is nothing. ​(Simplify your​ answer.) ​b) The probability that a randomly selected family has more than one cat is nothing. ​(Simplify your​ answer.) ​c) The probability that a randomly selected family has cats is nothing. ​(Simplify your​ answer.) ​d) Is this an example of​ classical, empirical, or subjective​ probability? Empirical probability Classical probability Subjective probability Thank you in advance!!

The numbers racket is a well‑entrenched illegal gambling operation in most large cities. One version works as follows: you choose one of the 1000 three‑digit numbers 000 to 999 and pay your local numbers runner a dollar to enter your bet. Each day, one three‑digit number is chosen at random and pays off $600 . The law of large numbers tells us what happens in the long run. Like many games of chance, the numbers racket has outcomes that vary considerably—one three‑digit number wins $600 and all others win nothing—that gamblers never reach “the long run.” Even after many bets, their average winnings may not be close to the mean. For the numbers racket, the mean payout for single bets is $0.60 ( 60 cents) and the standard deviation of payouts is about $18.96 . If Joe plays 350 days a year for 40 years, he makes 14,000 bets. Unlike Joe, the operators of the numbers racket can rely on the law of large numbers. It is said that the New York City mobster Casper Holstein took as many as 25,000 bets per day in the Prohibition era. That's 150,000 bets in a week if he takes Sunday off. Casper's mean winnings per bet are $0.40 (he pays out 60 cents of each dollar bet to people like Joe and keeps the other 40 cents). His standard deviation for single bets is about $18.96 , the same as Joe's.

(a) What is the mean of Casper's average winnings ?¯ on his 150,000 bets? (Enter your answer as dollars rounded to two decimal places.)

mean of average winnings=

What is the standard deviation of Casper's average winnings ?¯ on his 150,000 bets? (Enter your answer as dollars rounded to three decimal places.)

standard deviation=$

(b) According to the central limit theorem, what is the approximate probability that Casper's average winnings per bet are between $0.30 and $0.50 ? (Enter your answer rounded to four decimal places.)

approximate probability=

C++
1. The function removeAt of the class arrayListType removes an element from the list by shifting the elements ofthe list. However, if the element to be removed is at the beginning ofthe list and the list is fairly large, it could take a lot ofcomputer time. Because the list elements are in no particular order, you could simply remove the element by swapping the last element ofthe list with the item to be removed and reducing the length of the list. Rewrite the definition of the function removeAt using this technique.
2. The function remove of the class arrayListType removes only the first occurrence of an element. Add the function removeAll to the class arrayListType that would remove all occurrences of a given element. Also, write the definition ofthe function removeAll and a program to test this function.

From the textbook Data Structures using C++ by D. S. Malik

Q\ Suppose we have dice; the dice have six outcomes find the probability of the
following: -
a) What’s the probability of rolling a 4?
b) What’s the probability of rolling an odd number?
c) What’s the probability of rolling less than 6?
d) What’s the probability of rolling a 1 and 3?
e) What’s the probability of rolling a 0?
f) The probability of event a or c?
g) What’s the probability of rolling not event b?

Assume that the number of new visitors to a website in one hour is distributed as a Poisson random variable. The mean number of new visitors to the website is

2.3 per hour. Complete parts​ (a) through​ (d) below.

a. What is the probability that in any given hour zero new visitors will arrive at the​ website?

The probability that zero new visitors will arrive is__

b. What is the probability that in any given hour exactly one new visitor will arrive at the​ website?

The probability that exactly one new visitor will arrive is__

c. What is the probability that in any given hour two or more new visitors will arrive at the​ website?

The probability that two or more new visitors will arrive is__

d. What is the probability that in any given hour fewer than three new visitors will arrive at the​ website?

The probability that fewer than three new visitors will arrive is__

Alpha and Beta are divisions within the same company. The managers of both divisions are evaluated based on their own division’s return on investment (ROI). Assume the following information relative to the two divisions:

	Case
	1		2		3			4
Alpha Division:
Capacity in units		54,000		292,000		103,000			201,000
Number of units now being sold to outside customers		54,000		292,000		79,000			201,000
Selling price per unit to outside customers	$	96	$	42	$	67		$	48
Variable costs per unit	$	61	$	19	$	42		$	34
Fixed costs per unit (based on capacity)	$	20	$	8	$	23		$	10
Beta Division:
Number of units needed annually		10,200		69,000		18,000			64,000
Purchase price now being paid to an outside supplier	$	87	$	39	$	67	*		—

*Before any purchase discount.

Managers are free to decide if they will participate in any internal transfers. All transfer prices are negotiated.

1. Refer to case 1 shown above. Alpha Division can avoid $5 per unit in commissions on any sales to Beta Division.

	Identify the lowest and highest acceptable transfer prices: Lowest acceptable transfer price ? Highest acceptable transfer price ? ? ≤ Transfer price ≤ ? Will the managers agree to the trade? Yesradio button unchecked1 of 2 Noradio button unchecked2 of 2

2. Refer to case 2 shown above. A study indicates that Alpha Division can avoid $5 per unit in shipping costs on any sales to Beta Division.

	Identify the lowest and highest acceptable transfer prices: Lowest acceptable transfer price ? Highest acceptable transfer price ? ? ≤ Transfer price ≤ ? Loss in potential profits for the company ?

The random variable X, which represents the number of cherries in a cherry pie, has the following probability distribution:

a) Find the mean and the variance ² of the number of X

b) Find the mean _x and the variance of the mean of x̄ from a random sample of 36 countries Cherry.

c) Find the probability that the average number of cherries in 36 cherry countries will be less than 5.5.

Do it in python please

Write a program using functions and mainline logic which prompts the user to enter a number, then generates that number of random integers and stores them in a list. It should then display the following data to back to the user:

• The list of integers
• The lowest number in the list
• The highest number in the list
• The total sum of all the numbers in the list
• The average number in the list
• At a minimum, the numbers should range from 0 to 50, but you can use any range you like.

Helpful hint: don't forget about input validation loops and try/catch exceptional handling. Both are very useful when used in conjunction with functions.

The expected frequency value for a cell in a One-Way Frequency Table in which the categories are equally likely is:

• The ratio between the total number of subjects in the sample and the number of categories

• The probability for that cell

• The product between the observed frequency value and the probability for that cell

• The same as the observed frequency value