Considerthe following five -point summary for a variable that was obtained using 200 observations.

Minimum Q1 Median Q3 Maximum

57 77 89 101 121

a-1. interpret q1

a.Eighty percent of observations are less than 77,20% of the observations are greater than 77

b.Seventy five percent of observations are less than 77,25% of the observations are greater than 77

c.Twenty five percent of the observations are less than 77,75% of the observations are greater than 77

d.Twenty-five percent of the observations are less than 77,75% of the observations are greater than 77

a-2. interpret q3

a.Eighty percent of the observations are less than 101,20% of the observations are greater than 101

b.Seventy five percent of the observations are less than 101,25 of the observations are greater than 101

c.Twenty percent of observations are less than 101,80% of observations are greater than 101

d.Twenty five percent of observations are less than 101,75% of observations are greater than 101

B-1. calculate the interquartile range?

b-2. determine whether any outliners exist

a.No outliners exist

b.At least one outliner exists on the right side of distribution

c.At least one outliner exists on the right side of the distribution

d.Outliners exists on the both the left and right sides of distribution

c. is the distribution relatively symmetric? if not, comment on its skewness

a. the distribution is symmetric

b. the distribution is positively skewed

c. the distribution is the negatively skewed

d. symmetry or skewness cannot be determined with the available information

2.A sample of the salaries of assistant professors on the business faculty at a local university revealed a mean income of $96,000 with a standard deviation of $11,800. Assume that salaries follow a bell-shaped distribution. Use the empirical rule to answer the following questions

a.Approximately what percentage of the salaries fall between $84,200 and $107,800?

b.Approximately what percentage of the salaries fall between $72,400 and $119,600?

c.Approximately what percentage of the salaries are greater than $119,600?

3.The historical returns on a portfolio had an average return of 17% and a standard deviation of 9%. Assume returns on the portfolio follow a bell-shaped distribution. Use the empirical rule to answer the following questions

A.What percentage of returns were between 8 percent and 26 percent?

B.What percentage of returns were greater than 26 percent?

C.What percentage of returns were below -1 percent?