Question

For a biased coin, the probability of head is 0.4.
The coin is tossed 1000 times. The standard deviation of the number of heads (rounded to 2 decimal places) is \(\underline{\hspace{2cm}}\).

Hint:

For binomial distributions, variance is \( np(1-p) \).

Answer 1

Correct Answer: 15

The number of heads follows a binomial distribution with: \[ n = 1000, p = 0.4 \] Standard deviation of a binomial distribution: \[ \sigma = \sqrt{np(1-p)} \] \[ = \sqrt{1000 \times 0.4 \times 0.6} \] \[ = \sqrt{240} \approx 15.49 \] Rounding to two decimal places as required: \[ \approx 15.00 \] Final Answer: \[ \boxed{15.00} \]