Lemonbee’s Restaurant will serve a free dessert to customer’s on his/her birthday, provided that the person has registered for Lemonbee’s email list. Currently, there are 500 people who are on the email list and 4 of them have their birthday today. Lemonbee’s has 20 customers today. Assume that every customer who celebrates a birthday with free dessert is on Lemonbee’s email list.

a) Define X as the number of today’s customers at Lemonbee’s who have a birthday today. What is the distribution, parameter(s), and support of X?

b) What is the probability that at least one of the current customers has a birthday today?

c) It costs Lemonbee’s $2.35 to provide the free dessert. What is the expected value and standard deviation of the cost for Lemonbee’s free birthday desserts today.

d) Is there a valid approximation that can be used to calculate probabilities related to the number of today’s customers with birthdays today? If so, state the distribution, parameter(s) and support, along with the reason that the approximation is valid. If not, explain why not.

e) If you stated that there is a valid approximation in part e) use it to find the probability that 2 or 3 of today’s customers have their birthday today. If not, find the exact probability that 2 or 3 of today’s customers have their birthday today.

1, A police officer randomly selected 585 police records of larceny thefts. The accompanying data represent the number of offenses for various types of larceny thefts.

​(a) Complete the table below.

​(Round to three decimal places as​ needed.)

2, A baseball player hit 61 home runs in a season. Of the 61 home​ runs, 17 went to right​ field,20 went to right center field, 12 went to center​ field, 11 went to left center​ field, and 1 went to left field.

​(Round to three decimal places as​ needed.)

Consider a short multiple choice quiz with three items, and each item has four choices (only one of the choices is correct). Suppose that you are taking this quiz but you are completely and utterly unprepared for it. That means that you only option for the quiz is to guess the answers. Suppose you are thinking about the first item: what's the probability that you'll answer it incorrectly (hint: think about how many options there are, and how many of them are wrong)?

Now, list the "sample space" of all possible outcomes on this exam. Hint: here is one possible outcome: Correct, Correct, Wrong (or, CCW for short).

Using the format in #2 above, we actually haven't listed the entire sample space, because there are multiple ways to answer each item incorrectly! In order to calculate the probability of a particular outcome, we either need to list every single way to answer a problem wrong, or we can use the multiplication rule. These outcomes are all independent because guessing on problem #1 has no effect on your guess for problems #2 or #3. For example, P(Correct on the 1st, and Correct on the 2nd, and Wrong on the 3rd) = P(Correct on the 1st) * P(Correct on the 2nd) * P(Wrong on the Third). Find P(CCW).

Now, use your list from #2 and write the probability for each outcome next to it, using the same type of calcuation you did in #3.

Next, use your work from #4 to fill in the following table with the relevant probabilities, where x represents the number of items you answer correctly. Notice that the number of correct items will sometimes include more than one of the listed outcomes (what do you do with those numbers?)

In #5 above, you should have a probability distribution (which means that all probabilities are between 0 and 1, and the sum of the probabilities is 1). Check to make sure this is correct, fix any errors, and then explain why this situation fits the criteria for a binomial distribution.

Using the table you made in #5, determine the probability of getting at most 2 items correct on the quiz.

We don't need to calculate each probability by hand. It can be done in a spreadsheet: Using excel or sheets, you can type the command "BINOM.DIST" (in sheets, there is no dot) to help compute these probabilities. For example, the command "=BINOM.DIST(0,3,.25,0)" tells you the probability of getting 0 correct (# of "successes") out of three (# of trials) where the probability of getting one item correct is .25 (probability of a "success"), and we want exactly that number of correct items ("0" at the end of the command refers to the fact that we aren't adding up any probabilities, that the "cumulative" feature of the command is turned off). Verify, using this command, that each of the values in your table above is correct.

Now, you can also check the calculation you did in #7, by typing the following command: "BINOM.DIST(2,3,.25,1)", which means you want to get two correct (# of successes) out of three items (# of trials), where the probability of getting one item correct is .25 (probability of a success), and we are adding up the probabilities for all values below 2 as well (the cumulative spot is turned on when you type "1").

Finally, create a histogram of the distribution and copy it into your response.

(1) A company manufacturer pipes which was sent out to customers in losts of 1000.The manufacturer operates a sampling scheme whereby a random sample 10 is taken from each lot ready for despatch and they are released only if the number of defective pipes in the sample is less than 3.Otherwise, the whole lot of 1000 is rejected and reprocessed using the Binomial p.d.f.
(I) if 5% of all the pipes produced are known to be defective, how many lots will be rejected out of 1000 lots processed?
(ii)If the producer replaces his entire pipe producing machines causing the number of defective pipes to drop to only 1% and releases lots if the number of defective pipes in the sample of 10 less than 2.How many lots per 1000 will he expect to save?

(b) The demand for a particular type pump at an isolated place is random and independent of previous occurrences, but the average demand in a week (7dsys) is for 2.8 pumps .Further supplies are ordered each Tuesday morning and arrive on weekly plan on Friday morning . Last Tuesday morning only one pumps was in the stock, so the stores man ordered six more to come on Friday morning .
(I) Find the probability that one pump will still be in stock on Friday morning when new stock arrives,
(ii) Find the probability that stock will be exhausted and there will be unsatisfied demand for at least one pump by Friday.
(iii) Find the probability that one pump will be in stock this Friday morning and at least five will be in stock next Tuesday morning.

Tel-Skein is a call centre which fields all queries by customers of a national bank. Calls that are put through to operators who specialise in queries regarding ‘Lost or Stolen Debit Cards’ occur at random at a mean rate of 90 per hour.

(i) What is the probability distribution, including its parameter(s), of the number of calls arriving in this part of the call centre during a two-minute interval? (There is no need to calculate any probabilities in this part of the question).

(ii) Data have been collected on numbers of customers calling this part of the call centre in 100 two-minute periods and are summarised below. Use an appropriate test to investigate whether or not the data are consistent with your answer to part (i). Explain your method and conclusions carefully.

(iii)On Sundays, Tel-Skein runs a ‘skeleton-shift’ (i.e. it employs a reduced number of operators). As a result, operators specialising in ‘Lost or Stolen Debit Cards’ also have to field calls regarding ‘Bill Payments’. Calls regarding ‘Bill Payments’ occur at random at a mean rate of 150 per hour.

Assuming the call rate for ‘Lost or Stolen Debit Cards’ is unchanged, what is the probability that, during a one-minute period on Sundays, there will be between 3 calls and 5 calls; and what is the probability that the gap between calls will exceed 30 seconds?

American Airlines Flight 201 from New York's JFK Airport to LAX airport in Los Angeles uses a Boeing 767 which has 168 seats available for passengers. Because some people will reservations don't show up, airlines routinely overbook. Tha airline loses revenue if there are empty seats but if more passengers show up than there are seats, the airline must pay compensation to bumped passagers.

Use the start crunch Binomial calculator to answer the following based on the number of people with a reservation of 190.

Suppose American Airlines accepts 190 reservations for this flight.

Show calculation of n=190
a) What is the probability that exactly 168 passengers will show up?
Download and attach the Binomial calculator from StatCrunch into the discussion with your answer.( Use "option" in the left corner of graph and then use the Download "option)

b) What is the probability that more than 168 passengers will sjow up (some people will get bumped)?

c) Looking at the graph of the binomial calculator, what number of passengers is the most likely to show up?

Use trial and error in changing the value of "n" with the Binomial Calculator to answer the question below. try using values between 170 and 190 for n.

What is the number of reservations, n, the airline can accept so that the probability of more than 168 passengers showing up is as close as possible to 2% (but not higher than 2%) Download and attach the Binomial calculator from statcrunch which shows your answer.

"Some of you may have already picked up on this, but any discussion about the COVID-19 crisis will undoubtedly include a number of superlatives like “highest ever,” “most on record” and “unprecedented.”

Last week’s events were no exception. A head-spinning 6.6 million Americans filed new claims for unemployment benefits, bringing the two-week total to 10 million. That’s more than the combined populations of Los Angeles and Chicago."

The above is an excerpt from a Forbes article (Links to an external site.) posted April 6, 2020. If we are experiencing a higher rate of unemployment than the natural rate, what actions might the Federal Reserve take to improve the economy?

Solve using PYTHON 3 and use functions.

You have been hired by a restaurant named "Burger Shack" Per the client, you have the following information: the client’s name, burger’s name, time of the day, and the total bill. By the end of the day, your program will provide the following information:

1. Top three best clients (highest bills) 2. Name of the client with the second-to-last lowest bill 3. Busiest hour of the day (number of clients)

Assumptions: 1. doesn't handle more than 100 clients per day 2. this restaurant only has six types of burgers 3. restaurant hours are from 10:00am to 10:00pm

Suppose you are developing part of a social media website.

For the following, write down an algorithm that you would use to accomplish each one of these tasks. Your choice of search algorithm should be selected to complete each task as efficiently as possible

1. A search algorithm to determine the post with the highest number of positive votes (e.g likes)
2. A search algorithm to find all the posts made by a user on a specific date.
3. A search algorithm to determine the first post made by a specific user AFTER a specific date.
4. A search algorithm to find all the posts made by a user between two dates.
5. A search algorithm to find all posts containing a specific pattern of text.