Question

You are to take a multiple-choice exam consisting of 64 questions with 2 possible responses to each question. Suppose that you have not studied and so must guess (select one of the two answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test.
a. what kind of probability does x have?
b. What is your expected score on the exam?
c. Compare the variance and standard deviation of x.
d. based on your answers to parts b and c, is it likely that you would score over 50 on this exam?

Answer 1

Answer:

a) Binomial distribution.

b) Expected value = 32

c) Variance = 16

Standard deviation = 4

d) Getting a score of over 50 is not likely.

Step-by-step explanation:

Probability of getting a question right = (1/2) = 0.5

Probabilty of NOT getting a question right = 1 - 0.5 = 0.5

a) This kind of probability distribution approximates the binomial distribution the most. To solve for the probability of getting any number of questions correctly, the binomial distribution formula would give the required answer.

b) Expected score = mean = np = 64×0.5 = 32

c) Variance = np(1 - p) = 64 × 0.5 × 0.5 = 16

Standard deviation = √(variance) = √16 = 4

d) The mean score = 32.

Standard deviation = 4.

To score over 50, is at least 2 standard deviations away. And it is known that about 95% of the distribution lies between -2 and +2 standard deviations from the mean.

So, a score of over 50 is really not very likely.

Hope this Helps!!!