Question

The probability that a player will get 6-11 questions right on a trivia quiz are shown below. (See table)

Table 2: Player Proability
X 6, 7, 8, 9, 10, 11,
P(X) 0.05, 0.1, 0.3, 0.1, 0.15, 0.3
Find the mean. Find the variance. Find the standard deviation.

Answer 1

Anములు, Given Table X 6 7 8 9 10 ll PCXsx) 0.05 0.1 0.3 0.1 0.15 0.3 ? 600.05)+7(0.1) +800-3)+9(0:1) +1000-15) 1. Find the mean ECHIP - ExpÝ) = 660.05)+7(0-1) +860 &=6 +11 (0.3) 19.1) 2. Find the variance ECx2) 3 x PCX) = 6CO-05) +720.1) +8(0.3)+9%20-1) +1020-15) +11 (0.3) = 85.3 Xc6 variance - EC42) - ECX) = 85.3-9-11° 3. find the standard deviation standard deviation Jvariance = 52.49 - 11:57]

Answer 2

SOLUTION :

Mean, m 

= ∑ p(x) * X  

= 0.05*6 + 0.1*7 + 0.3*8 + 0.1*9 + 0.15*10 + 0.3 *11

= 9.1 (ANSWER)

Variance

= ∑ p(x)(m - X)^2 

= 0.05(9.1 - 6)^2 + 0.1(9.1 - 7)^2 + 0.3(9.1 - 8)^2 + 0.1(9.1 - 9)^2 + 0.15(9.1 - 10)^2 + 0.3(9.1 - 11)^2

= 2.49 (ANSWER)

SD 

= sqrt(Variance)

= sqrt(2.49)

= 1.578 (ANSWER).