The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 220 customers on the number of hours cars are parked and the amount they are charged.

How many unmarried male shoppers might I possibly reach with advertising campaigns for the following combinations of TV​ shows? Keep in​ mind, we want to avoid​ "double counting" males who may watch both channels. For​ simplicity, though, assume that the chance a male watches one cable channel does not influence the chances they will watch a different channel.

When two events are considered to be unrelated to one​ another, the probability of them BOTH happening is just​ "Probability of Event

​A"times×​"Probability

of Event​ B". This is represented as

​"Upper P left parenthesis Upper A intersect Upper B right parenthesisP(A∩B)​".

The combined probability of the events is​ "Probability of Event

​A"plus+​"Probability

of Event

​B"minus−​"Upper P left parenthesis Upper A intersect Upper B right parenthesisP(A∩B)​".

Multiply the the combined probability of watching both channels by the total number of unmarried male shoppers. Use the provided table above to answer the question.

Fill in the table below. ​(Round to the nearest whole​ number.)

Among married principal​ shoppers, (---------)1 is the ratio of females to males. ​(Round to two decimal​ places.)

Among married principal shoppers who watch Comedy​ Central, (-------------)​:1 is the ratio of females to males. ​(Round to two decimal​ places.)

The percentage of all​ SyFy-watching principal shoppers that are married is calculated as​ follows:

% of all SyFy dash watching Principal Shoppers are Married = equals StartFraction Female Married Pricipal Shopper Subscript SyFy + Male Married Pricipal Shopper Subscript SyFy Over All Principal Shoppers Subscript SyFy EndFraction% of all SyFy

(---------------) % of all​ SyFy-watching principal shoppers are married. ​(Round to two decimal​ places.)

Approximately​ speaking, do married men or married women principal shoppers say they watch more of the cable channels listed​ here?

Fill in the table below. ​(Round to two decimal​ places.)

A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 49 calls per hour. The service rate per line is 27 calls per hour.

1. What is the probability that 0, 1, 2, and 3 access lines will be in use? Round your answers to 4 decimal places.
   

   j	Pj
   0
   1
   2
   3

   
   
2. What is the probability that an agent will be denied access to the system? Round your answers to 4 decimal places.
   
   
   
3. What is the average number of access lines in use? Round your answers to 4 decimal places.
   
   L =  
   
4. In planning for the future, management wants to be able to handle λ = 57 calls per hour; in addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have?
   
   lines will be necessary.

A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 45 calls per hour. The service rate per line is 23 calls per hour.

1. What is the probability that 0, 1, 2, and 3 access lines will be in use? Round your answers to 4 decimal places.

2. jP_j

3. 0

4. 1

5. 2

6. 3

7. What is the probability that an agent will be denied access to the system? Round your answers to 4 decimal places.
   
   
   
8. What is the average number of access lines in use? Round your answers to 4 decimal places.
   
   L =  
   
9. In planning for the future, management wants to be able to handle λ = 53 calls per hour; in addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have?
   
   lines will be necessary.

please use Poisson Processes to answer the below question :

Q. Voters arrive at a polling booth in a remote Queensland town at an average rate of 30

per hour. There are two candidates contesting the election and the town is divided. Candidate

A is far more popular, and is known that any voter will vote for her with probability 0.85.

(a) The electoral officer arrived exactly 6 minutes late to open the booth, and one voter was

waiting outside. What is the probability that the voter had been waiting for more than 5

minutes? You may assume that they did not arrive before the polling booth was meant to

open.

(b) Due to social distancing measures, voters that arrive within a minute of another voter must

wait outside. What is the probability that, when you turn up to vote, you need to wait

outside?

(c) What is the expected number of votes that Candidate A will receive during the 8 hour

voting period?

(d) By the time the election has closed, exactly 8 hours after it started, exactly 238 voters had

cast their vote and Candidate A had won 198 votes to 40. Use a normal approximation

to compute the probability that the candidate A had received enough votes to win in the

first 4 hours of the election. Ensure you validate the assumptions required to use a normal

approximation and apply a continuity correction.

In 2012, the percent of American adults who owned cell phones and used their cell phones to send or receive text messages was at an all-time high of 80%. Assume that 80% refers to the population parameter. More recently in 2015, a polling firm contacts a simple random sample of 110 people chosen from the population of cell phone owners to confirm the percent who use their phone to text. The firm askes each person "do you use your cell phone to send or receive texts Yes or No. "

a) Verify that the conditions are met so that the central limit theorem can apply to p̂

b) What is the approximate distribution of p̂, the proportion of cell phone owners in the 2015 sample who use their cell phone to text? Give the shape, mean, and standard deviation.

c) What is the probability that p̂ is between 78% and 82%: what is P(0.78 < p̂ < 0.82). In other words, what is the probability that p̂ estimates π within 2% of 0.8?

d) Suppose the polling firm increased the number of people in its sample to 1100 people. Now what is the probability that p̂ is between 78% and 82%? In other words, what is the probability that p̂ estimates π within 2%?

e) Which sample size (110 or 1100) gives a more accurate estimate of the population proportion of cell users who text?

X ~ N(50, 13). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums.

• Part (a)

  Sketch the distributions of X and X on the same graph.

  • A	B)
    C)D)

• Part (b)

  Give the distribution of X. (Enter an exact number as an integer, fraction, or decimal.)

  X ~ ____(____,____)

• Part (c)

  Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.)

  P(X < 50) = ________

• Part (d)

  Find the 30th percentile. (Round your answer to two decimal places.)

• _________.

• Part (e)

  Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.)

  P(48 < X < 54) = _________

• Part (f)

  Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.)

  P(17 < X < 48) = ___________

• Part (g)

  Give the distribution of ΣX.
  ΣX ~ ______(_____,_____)

• Part (h)

  Find the minimum value for the upper quartile for ΣX. (Round your answer to two decimal places.)

• ________.

• Part (i)

  Sketch the graph, shade the region, label and scale the horizontal axis for ΣX, and find the probability. (Round your answer to four decimal places.)

  P(1200 < ΣX < 1350) = ___________

A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 47 calls per hour. The service rate per line is 25 calls per hour.

1. What is the probability that 0, 1, 2, and 3 access lines will be in use? Round your answers to 4 decimal places.
   

   j	Pj
   0
   1
   2
   3

   
   
2. What is the probability that an agent will be denied access to the system? Round your answers to 4 decimal places.
   
   
   
3. What is the average number of access lines in use? Round your answers to 4 decimal places.
   
   L =
   
4. In planning for the future, management wants to be able to handle λ = 55 calls per hour; in addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have?
   
   lines will be necessary.

(1 point) A hockey player is to take 3 shots on a certain goalie. The probability he will score a goal on his first shot is 0.35. If he scores on his first shot, the chance he will score on his second shot increases by 0.1; if he misses, the chance that he scores on his second shot decreases by 0.1. This pattern continues to on his third shot: If the player scores on his second shot, the probability he will score on his third shot increases by another 0.1; should he not score on his second shot, the probability of scoring on the third shot decreases by another 0.1.

A random variable ?X counts the number of goals this hockey player scores.

(a) Complete the probability distribution of ?X below. Use four decimals in each of your entries.

(b) How many goals would you expect this hockey player to score? Enter your answer to four decimals.

?(?)=E(X)=

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(c) Compute the standard deviation the random variable ?X. Enter your answer to two decimals.

??(?)=SD(X)=

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Equation Editor