Assume Binomial Distribution with n = 15 and p = 0.5. Please show your answers to 4 decimal places.

P(X == 4) = P(X 4) = P(X << 4) = P(X >> 4) = P(X 4) =

The probability that the San Jose Sharks will win any given agame is 0.4729 based on a 29-year win history of 1,049 wins out of 2,218 games played. (As of the end of the 2020-2021 Season via San Jose Sharks .) An upcoming monthly schedule contains 12 games. The conditions of a binomial distribution are met:

• The number of upcoming games is 12 (fixed trials)
• The outcome of one game doesn't affect other games (independent trials)
• Each game has a win/lose outcome (binary outcomes)
• The probability of a "success" is the same for each trial. (p=0.4729p=0.4729)

Use the scenario above to determine the expected value () and selected probabilities below.

1. The expected number of wins for the upcoming schedule is?

==

2. What is the probability that the San Jose Sharks will win exactly six games in the upcoming schedule? P(X=6)=P(X=6)=

3. What is the probability that the San Jose Sharks win at least five games in the upcoming schedule? P(X5)=P(X5)=

4. What is the probability that the San Jose Sharks will win more than seven games in the upcoming schedule? P(X>7)=P(X>7)=

A local county has an unemployment rate of 5.6%. A random sample of 15 employable people are picked at random from the county and are asked if they are employed. The distribution is a binomial. Round answers to 4 decimal places.

a) Find the probability that exactly 2 in the sample are unemployed.

b) Find the probability that there are fewer than 4 in the sample are unemployed.

c)Find the probability that there are more than 3 in the sample are unemployed.

d)Find the probability that there areat most4 in the sample are unemployed.

A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.123. Consider your next 45 purchases that produce a game piece. Calculate the following:

For parts (a) through (d), express your answer as a decimal with 4 decimal places.

a) What is the probability that you win 5 prizes?

b) What is the probability that you win more than 7 prizes?

c) What is the probability that you win between 4 and 7 (inclusive) prizes?

d) What is the probability that you win 3 prizes or fewer?

An actress has a probability of getting offered a job after a try-out of 0.01. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent. Find the probability she will need to attend more than 5 try-outs.

73% of a basketball player's free throw shots are successful. In a given game, find the probability that (a) her first successful freethrow shot is shot number four. (b) she makes her first successful freethrow within the first two shots. (c) she takes more than seven shots to make her first successful free throw.

1 out of every 5 kid's meals contain a toy car. Find the probability that (a) You must purchase eight kid's meals to find a toy car. (b) You must purchase fewer than eight kid's meals to find a toy car. (c) A toy car is not in any of the first five kid's meals you purchase

On average, a baking student accidentally drops three pieces of egg shell into the batter of every two cakes made. The conditions of a Poisson Distribution are met:

• The baking of a cake does not affect the outcome of any other cake. (independent events)
• The average rate is constant: 3 pieces per 2 cakes (rate=32=1.5)(rate=32=1.5)
• Baking (and dropping eggshells) is a sequential process. (Two events cannot occur at the same time)

Use the scenario above to determine the expected value () and selected probabilities below.

1. On average, how many egg shells do you expect to be in a single cake? == (decimal answers only)
2. If a single cake is bought, what is the probability of finding 0 egg shell pieces in it? P(X=0)=P(X=0)= (include four decimal places)
3. If a single cake is bought, what is the probability of finding more than two egg shell pieces in it? P(X>2)=P(X>2)= (include four decimal places)

Complaints about an Internet brokerage firm occur at a rate of 1.1 per day.

Round all results to THOUSANDTHS place. Then express answers in percent form (i.e. 30.0% instead of 0.3)

(a) What is the probability of receiving 0 complaints in a 3-day period? % (b) What is the probability of receiving 1 complaint in a 3-day period? % (c) What is the probability of receiving 2 complaints in a 3-day period? % (d) What is the probability of receiving 3 complaints in a 3-day period? % (e) What is the probability of receiving 4 complaints in a 3-day period? % (f) What is the probability of receiving less than or equal to 4 complaints in a 3-day period? % (g) What is the probability of receiving more than 4 complaints in a 3-day period?

Complaints about an Internet brokerage firm occur at a rate of 1.5 per day.

Round all results to THOUSANDTHS place. Then express answers in percent form (i.e. 30.0% instead of 0.3)

(a) What is the probability of receiving 0 complaints in a 3-day period? % (b) What is the probability of receiving 1 complaint in a 3-day period? % (c) What is the probability of receiving 2 complaints in a 3-day period? % (d) What is the probability of receiving 3 complaints in a 3-day period? % (e) What is the probability of receiving 4 complaints in a 3-day period? % (f) What is the probability of receiving less than or equal to 4 complaints in a 3-day period? % (g) What is the probability of receiving more than 4 complaints in a 3-day period? %

A court stenographer makes six typographical errors per hour on average. Find the probability that (a) The stenographer makes exactly thirteen typographical errors during an hour long court case. (b) The stenographer makes no more than seven typographical errors during an hour long court case. (c) The stenographer makes seven or more typographical errors during an hour long court case. Round all answers to four decimal places.

Occasionally an airline will lose a bag. A small airline has found it loses an average of 2.2 bags each day. Find the probability that, on a given day, (a) The airline loses exactly two bags. (b) The airline loses fewer than two bags. (c) The airline loses more than five bags. Round all answers to four decimal places.