Students in a class take a quiz with eight questions. The number x of questions

Question

Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete parts (a) through (e). x 0 1 2 3 4 5 6 7 8 P(x) 0.030.03 0.010.01 0.060.06 0.050.05 0.140.14 0.230.23 0.240.24 0.170.17 0.070.07 (a) Use the probability distribution to find the mean of the probability distribution. muequals=nothing (Round to the nearest tenth as needed.) (b) Use the probability distribution to find the variance of the probability distribution. sigma squared2equals=nothing (Round to the nearest tenth as needed.) (c) Use the probability distribution to find the standard deviation of the probability distribution. nothing (Round to the nearest tenth as needed.) (d) Use the probability distribution to find the expected value of the probability distribution. nothing (Round to the nearest tenth as needed.)

Explanation / Answer

Given x. P(x)

0. 0.03

1. 0.01

2. 0.06

3. 0.05

4. 0.14

5. 0.23

6. 0.24

7. 0.17

8. 0.07

a) Xmean = E(X) = 0*0.03 + 1*0.01+ 2*0.06 + 3*0.05 + 4*0.14 + 5*0.23 + 6*0.24 + 7*0.17 + 8*0.07 = 5.18

B) Variance = (x^2 * P(x)) - Mean^2=(0^2*0.03+1^2*0.01+2^2*0.06+3^2*0.05+4^2*0.14+5^2*0.23+6^2*0.24+7^2*0.17+8^2*0.07)-5.18^2

Varience =30.15-26.8324=3.3176

C)Standred deviation=1.8214

D) Expected value is 5.18

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