Question

A test consists of 100 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers. mean: 20; standard deviation: 4 mean: 20; standard deviation: 4.47 mean: 50; standard deviation: 7.70 mean: 50; standard deviation: 4

Answer 1

Answer: Mean = 20 and standard deviation = 4

Explanation:

Let x represents the success of getting the correct answer.

Here, the total number of trials(n) = 100

The probability of getting the correct answer, p = 1/5

Thus, the mean of the number of correct answer,

`\mu_x= np`

`\mu_x= 100* 1/5`

`\mu_x= 20`

Now, the standard deviation,
`\sigma_x= √(n* p* (1-p))`

`\sigma_x= √(100* 1/5* 4/5)`

`\sigma_x= √(16)`

`\sigma_x= 4`

Thus, First option is correct.