Answer:
(a) The expected score is 12.8
(b) The standard deviation is 3.2 and variance is 10.24
Step-by-step explanation:
Consider the provided information.
You are to take a multiple-choice exam consisting of 64 questions with 5 possible responses to each question.
Here n=64 p=1/5 and q=1-1/5=4/5
Part (a) we need to find the expected score on the exam.
Expected = np
Expected score = number of questions × P(right)
[tex]Score = 64 \times \frac{1}{5} = 12.8[/tex]
Hence, the expected score is 12.8
Part (b) Compute the variance and standard deviation of x.
Standard Deviation: [tex]\sigma =\sqrt{npq}[/tex]
Now calculate the standard deviation as shown:
[tex]\sigma =\sqrt{64\times \frac{1}{5}\times \frac{4}{5}}[/tex]
[tex]\sigma =\sqrt{\frac{256}{25}}[/tex]
[tex]\sigma =\frac{16}{5}=3.2[/tex]
Variance: [tex]\sigma^2 =npq[/tex]
[tex]\sigma^2 =64\times \frac{1}{5}\times \frac{4}{5}[/tex]
[tex]\sigma^2 =\frac{256}{25}[/tex]
[tex]\sigma^2 =10.24[/tex]
Hence, the standard deviation is 3.2 and variance is 10.24
