Question

A die is thrown 100 times, then the standard deviation of getting an even number is

• A. 10
• B. 5
• C. 20
• D. 15

Hint:

For binomial distribution, the standard deviation is \( \sqrt{npq} \).

Answer 1

The Correct Option is B

Step 1: Probability of getting an even number.
The even numbers on a die are \( 2, 4, 6 \). So, the probability of getting an even number is \[ P(\text{even}) = \frac{3}{6} = \frac{1}{2} \] Step 2: Use the binomial distribution formula.
The standard deviation for a binomial distribution is given by \[ \sigma = \sqrt{npq} \] where \( n \) is the number of trials, \( p \) is the probability of success, and \( q = 1 - p \).
Step 3: Calculate the standard deviation.
Here, \( n = 100 \), \( p = \frac{1}{2} \), and \( q = \frac{1}{2} \). Thus, \[ \sigma = \sqrt{100 \times \frac{1}{2} \times \frac{1}{2}} = \sqrt{25} = 5 \] Step 4: Conclusion.
The standard deviation is 5.