Students in a class take a quiz with eight questions. The number x of questions
ID: 2928853 • Letter: S
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)
0.03
0.02
0.05
0.06
0.12
0.22
0.28
0.14
0.08
(a) Use the probability distribution to find the mean of the probability distribution.
muequals=5.2
(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.)
x
0
1
2
3
4
5
6
7
8
Open in StatCrunch + Copy to Clipboard + Open in Excel +P(x)
0.03
0.02
0.05
0.06
0.12
0.22
0.28
0.14
0.08
Explanation / Answer
answer
mean = Sum x * p(x) = 0 * 0.03 + 1 * 0.02 + 2 * 0.05 + 3* 0.06+4*0.12+5*0.22+6*0.28+7*0.14+8*0.08 = 5.18
variance = sum x^2 p(x) - M^2 = 0^2 * 0.03 + 1^2 * 0.02 + 2^2 * 0.05 + ... - M^2
=0+0.02+0.2+0.54+1.92+5.5+10.08+6.86+5.12-(5.18)^2
=30.24-(5.18)^2
=30.24-26.8324
=3.4076