# Question: 1 consider the following data for all los angeles rams...

###### Question details

1) Consider the following data for ALL Los Angeles Rams home games for the 2018 NFL season:

Points |
Offensive yards |

34 |
432 |

35 |
521 |

38 |
556 |

29 |
416 |

36 |
456 |

54 |
455 |

23 |
407 |

48 |
377 |

a) Compute the points and offensive yards. (2 points)

b) Compute the standard deviation of points and offensive yards. (5 points)

c) Compute the covariance between points and offensive yards. Provide an interpretation of the covariance. (7 points)

d) Compute the correlation coefficient between points and offensive yards. (3 points)

2) Suppose that at a particular university the average GPA is 2.75 and the standard deviation of GPAs is 0.5.

a) Compute the z-score of a student with a GPA of 2.2. (1 points)

b) Compute the z-score of a student with a GPA of 4.0. (1 points)

3) Suppose a city receives precipitation (measured in inches) each year subject to the following probability distribution: X~N(70,49).

a) Compute the probability that the city will receive less than 90 inches in a year. (2 points)

b) Compute the probability that the city will receive more than 60 inches in a year. (2 points)

c) Compute the probability that the city will receive between 49 and 91 inches in a year. (2 points)

4) Consider the following population of individuals along with their corresponding annual income: A earns $30K, B earns $36K, C earns $49 and D earns $60K.

a) Suppose one wants to know the mean annual income of the population and draws a random sample of two individuals (without replacement). List the possible samples and the corresponding sample mean annual income. Also, compute the expected value of the sample mean annual income, E(x). (4 points)

b) Suppose one wants to know the mean annual income of the population and draws a random sample of three individuals (without replacement). List the possible samples and the corresponding sample mean annual income. Also, compute the expected value of the sample mean annual income, E(x). (4 points)

c) How does the larger sample size affect the expected value of the sample means? (2 points)

d) How does the larger sample size affect the dispersion of the possible sample means. (2 points)