Question

a quiz consists of 640 true or false questions. if the student guesses on each question, what is the mean number of correct answers?
a. 320
b. 0
c. 640
d. 128

Explanation:

Step1: Identify the distribution parameters

This is a binomial distribution problem. The number of trials \(n = 640\), and the probability of success (correct answer) \(p=\frac{1}{2}\) (since it's true - false, 2 options).

Step2: Use the formula for the mean of a binomial distribution

The formula for the mean of a binomial distribution is \(\mu=np\). Substitute \(n = 640\) and \(p=\frac{1}{2}\) into the formula: \(\mu=640\times\frac{1}{2}\).

Step3: Calculate the value

\(640\times\frac{1}{2}=\frac{640}{2}=320\).

Answer:

A. 320