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SPC have found from experience that the mean weight of William pears is 205 grams and there is a standard deviation of 18 grams.

SPC have found from experience that the mean weight of William pears is 205 grams and there is a standard deviation of 18 grams. If farmer Brown had a harvest last year of 12,780 pears, how many pears would have been between 195 and 225 grams?

(Show suitable diagrams to accompany your calculations)
5 + 5 =10Marks

Question 2
Given a large population whose mean is 500 and whose standard deviation is 100, find the probability that a random sample of 361 has a mean that lies between 495 and 515.

(Show suitable diagrams to accompany your calculations)
5 + 5 = 10marks

Question 3
The number of salespersons employed by a car dealer varies from a low of four to a high of eight. The sales manager wanted to know if he could determine the number of cars sold in a week based on the number of salespeople. To this end he identified eight weekly periods, in the last five months, during which there were no special incentive programs in use. The following figures were revealed:

Week 1 2 3 4 5 6 7 8
Salespeople 5 6 5 4 7 6 5 8
Car sales 10 20 18 10 21 15 13 22

a) Plot the data on a scatter diagram
b) Compute an equation for the line of best fit using least squares
c) Plot the regression line from part (b) on the scatter diagram from part (a)
d) Estimate the number of cars that would be sold next week if the dealer employs six salespeople.

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