Question

The probability that an individual is left-handed is 0.16. In a class of 10 students, what is the mean and standard deviation of the number of left-handed students?

• A. 1.6 and 1.226 respectively
• B. 1.6 and 1.159 respectively
• C. 2.6 and 1.26 respectively
• D. 4 and 1.26 respectively

Hint:

For binomial distribution: \(\mu = np\), \(\sigma = \sqrt{npq}\).
Use these formulas for problems involving counts of successes.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The number of left-handed students follows a binomial distribution.

Step 2: Key Formula or Approach:
For binomial distribution, mean \(\mu = np\), variance \(\sigma^2 = npq\).

Step 3: Detailed Explanation:
Given \(n = 10\), \(p = 0.16\), so \(q = 0.84\).
Mean \(\mu = np = 10 \times 0.16 = 1.6\).
Variance \(\sigma^2 = npq = 10 \times 0.16 \times 0.84 = 1.344\).
Standard deviation \(\sigma = \sqrt{1.344} \approx 1.159\).
Thus, mean = 1.6 and standard deviation = 1.159.
This matches option (B).
Option (A) has 1.226 which is incorrect.
The binomial distribution is appropriate here.