Answer:
(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
