Question

A true-false quiz with 10 questions was given to a statistics class. Following is the probability distribution for the score of a randomly chosen student. Find the mean score and interpret the result. Round the answers to two decimal places as needed.

Answer 1

Answer:

hi your question is incomplete here is the complete question attached to the answer is the probability distribution of the randomly chosen student

answer : 7.5

Step-by-step explanation:

The mean score of the probability distribution

= summation of (x * P(x) )

= ( 5* 0.05 ) + ( 6*0.16 ) + ( 7 * 0.32 ) + ( 8 * 0.26 ) + ( 9 * 0.13 ) + ( 10* 0.08)

= 0.25 + 0.96 + 2.24 + 2.08 + 1.17 + 0.8

= 7.5  the mean score is 7.5

This result means that the mean if more students were given the True -false  quiz with 10 questions the mean score would still be 7.5

Answer 2

Answer:

$E(X)=\sum_{i=1}^n X_i P(X_i)$  

And if we use the values obtained we got:  

$E(X)=5*0.05 +6*0.15 +7*0.33 +8*0.28+ 9*0.12 +10*0.07=7.48$  

For this case this value means that the expected score is about 7.48

Step-by-step explanation:

For this case we assume the following probability distribution:

X         5       6         7       8        9        10

P(X)   0.05   0.15  0.33  0.28   0.12   0.07

First we need to find the expected value (first moment) and the second moment in order to find the variance and then the standard deviation.

In order to calculate the expected value we can use the following formula:  

$E(X)=\sum_{i=1}^n X_i P(X_i)$  

And if we use the values obtained we got:  

$E(X)=5*0.05 +6*0.15 +7*0.33 +8*0.28+ 9*0.12 +10*0.07=7.48$  

For this case this value means that the expected score is about 7.48

In order to find the standard deviation we need to find first the second moment, given by :  

$E(X^2)=\sum_{i=1}^n X^2_i P(X_i)$  

And using the formula we got:  

$E(X^2)=(5^2 *0.05)+(6^2 *0.15)+(7^2 *0.33)+(8^2 *0.28)+ (9^2 *0.12 +(10^2 *0.07))=57.46$  

Then we can find the variance with the following formula:  

$Var(X)=E(X^2)-[E(X)]^2 =57.46-(7.48)^2 =1.5096$  

And then the standard deviation would be given by:  

$Sd(X)=\sqrt{Var(X)}=\sqrt{1.5096}=1.229$