Question

4. In a race with 8 horses, in how many ways can the race end with the first, second, and third place winners?

5. For one week in May, an insurance agent kept records of the number of prospective clients (x) with whom she had consulted and the number of them who had purchased a policy (y).

a. Find the correlation coefficient r

b. Find the coefficient of determination ?2

c. What percentage of the variation in the number of prospective clients who purchased a policy can be explained by the corresponding variation in the number of consultations?

x y

11 3

5 2

7 3

25 10

8 6

Answer 1

Solution:

here we have to gove the answer for this problem such as

4. In a race with 8 horses, in how many ways can the race end with the first, second, and third place winners?

now formula for this is nCx = n! / ((n-x)!*(x!))

Here value of n= 8 and x= 3

therefore we say that

answer= 56

56 ways the race end with the first, second, and third place winners.

now we solve remaning problem using the minitab statistical software as below

a) formula for correlation

correlation coefficient r = = 0.889

here we say that there is strong and positive correlation between x and y because it is close to +1

b) now

coefficient of determination ?2

= 0.7903

c)

therefore we say that 79.03% percentage of the variation in the number of prospective clients who purchased a policy can be explained by the corresponding variation in the number of consultations

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