Business statistics

Assignment 3

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Information about mutual funds provided by Morningstar Investment Research includes the type of mutual fund (Domestic Equity, International Equity, or Fixed Income) and the Morningstar rating for the fund. The rating is expressed from 1-star (lowest rating) to 5-star (highest rating). Suppose a sample of 25 mutual funds provided the following counts:

  • Sixteen mutual funds were Domestic Equity funds.
  • Thirteen mutual funds were rated 3-star or less.
  • Seven of the Domestic Equity funds were rated 4-star.
  • Two of the Domestic Equity funds were rated 5-star.

Assume one of these 25 mutual funds will be randomly selected in order to learn more about the mutual fund and its investment strategy.

  • What is the probability of selecting a Domestic Equity fund?
  • What is the probability of selecting a fund with a 4-star or 5-star rating?
  • What is the probability of selecting a fund that is both a Domestic Equity and a fund with a 4-star or 5-star rating?
  • What is probability of selecting a fund that is a Domestic Equity fund or a fund with a 4-star or 5-star rating?

Employee retention is a major concern for many companies. A survey of Americans asked how long they have worked for the current employer (Bureau Labor Statistics website). Consider the following example of sample data of 2,000 college graduates who graduated five years ago.

Time with Current Employers (years) Number
1 506
2 390
3 310
4 218
5 576

Let x be the random variable indicating the number of years the respondent has worked for her/his current employer.

a.Use the data to develop an empirical discrete probability distribution for x.

b.What is the probability that a respondent has been at her/his current place of employment for more than 3 years?

3.The Chamber of Commerce in a Canadian city has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received a 3-point scale on typical meal price (1 least expensive to 3 most expensive) and quality (1 lowest quality to 3 greatest quality). A crosstabulation of the rating data is shown. Forty-two of the restaurants received a rating of 1 on quality and 1 on meal price, 39 of the restaurants received a rating of 1 on quality and 2 on meal price, and so on. Forty-eight of the restaurants received the highest rating of 3 on both quality and meal price.

  Meal Price (y)  
Quality (x) 1 2 3 Total
1 42 39 3 84
2 33 63 54 150
3 3 15 48 66
Total 78 117 105 300

a.Develop a bivariate probability distribution for quality and meal price of a randomly selected restaurant in this Canadian city. Let x = quality of rating and y = meal price.

b.Compute the expected value and variance for quality rating, x.

c.Compute the expected value and variance for meal price, y.

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