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**EXPERIENCE 5 DUE**

**Please where applicable can you show the step by step working.**

About 24% of flights departing from New York’s John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct?

You get two attempts at this problem so choose wisely. If you submit this once and do not receive 5 points in your Gradebook then you did not get it right so try again.

- We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
- We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another.
- We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
- We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability.

Suppose you are a lawyer representing a Hispanic individual in a criminal trial. Twelve jurors are randomly selected by the state from a population that you know to be 40% Hispanic.

a. How many jurors would you expect to be Hispanic?

b. The select process produces a jury with 3 Hispanic individuals What proportion of the jury is Hispanic? (Enter your answer as a decimal, rounded to four decimal places)

c. Use the binomial distribution and find the probability that 3 or fewer jurors would be Hispanic.

d. Create a graph of the distribution with the area corresponding to the previous answer shaded in. Choices for creating a graph include: Excel, Binomial Distribution Calculator (in resources menu), TI-84 (take a pic), hand drawn, other software, websites. Upload your finished graph below. No file chosen

e. Use Statistics to make an argument to the court on behalf of your client. Structure your essay as a paragraph that contains the following:

Your Honor,

Explain why random sampling in this situation of juror selection relates the expected sample proportion to the population proportion.

Compare the expected value to the actual sample proportion.

Show that the requirements for a binomial experiment are met in this situation, implying that the binomial distribution can be used.

Identify the values for n,p, and x for this situation

Interpret the answers to parts c. and d. and submit them as evidence.

Use this to argue that the juror selection was likely to be random or not likely to be random (depending on your answer to part c).

Request a new jury be selected or accept the selected jury (depending on your answer to part c)

Respectfully,

[Your Name]

- About 8% of the population has a particular genetic mutation. 1000 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 1000.

- About 5% of the population has a particular genetic mutation. 700 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 700. Round your answer to three decimal places

- Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some form of technology like Excel or StatDisk to find the probability distribution given the probability p=0.217p=0.217 of success on a single trial.
*(Report answers accurate to 4 decimal places.)* - A small regional carrier accepted 21 reservations for a particular flight with 18 seats. 10 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 46% chance, independently of each other.

*(Report answers accurate to 4 decimal places.)*Find the probability that overbooking occurs.

Find the probability that the flight has empty seats. - After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only three women among the last 18 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.
Help her address the charge of gender discrimination by finding the probability of getting three or fewer women when 18 people are hired, assuming that there is no discrimination based on gender.

*(Report answer accurate to 8 decimal places).*

*P*(at most three) =Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge?

k |
P(X = k) |

0 | |

1 | |

2 | |

3 | |

4 | |

5 |

- no, this does not support a charge of gender discrimination
- yes, this supports a charge of gender discrimination

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