3. The variance of a set of positive numbers p.(p-5).(p-2), (p-3) (2p-5)is 5.84. (a) Calculate the value of p.

(a) p = 7

Step-by-step explanation:

The given parameters are;

p, (p - 5), (p - 2), (p - 3), and (2·p - 5) is 5.84

(a) Therefore we have;

The mean of the numbers = (p + (p - 5) + (p - 2) + (p - 3) + (2·p - 5))/5 = (6·p - 15)/5

The mean of the numbers = (6·p - 15)/5 = 6/5·p - 3

Using an online tool, we have;

The variance = (p - (6/5·p - 3))² + ((p - 5) - (6/5·p - 3))² + ((p - 2) - (6/5·p - 3))² + ((p - 3) - (6/5·p - 3))² + ((2·p - 5) - (6/5·p - 3))²/5 = 4/25·p² - 4/5·p + 18/5 = 5.84

Therefore, we have;

4/25·p² - 4/5·p + 18/5 = 5.84

4/25·p² - 4/5·p + 18/5 - 5.84 = 0

4/25·p² - 4/5·p - 2.24 = 0

Using the quadratic formula, we have;

p = (4/5 ± √((4/5)² - 4× 4/25×(-2.24)))/(2 × 4/25)

Which gives;

p = 7, or p = -2

Given that the numbers are positive, we have the only solution as p = 7

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