In a manufacturing plant, the probability of making a defective bolt is 0.1. Find the mean and standard deviation of defective bolts in a total of 900 bolts.

In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectively 

(A) 90 and 9,    (B) 9 and 90,    (C) 81 and 9,    (D) 9 and 81. 

(GATE 2000) 

Answer: (A) 90 and 9 

Explanation: 

Let $X$ be a random variable that denotes the number of defective bolts. 

Here, $X$ follows a binomial distribution with the parameters $p = 0.1$ and $n = 900$. 

Therefore, mean $= E(X) = n \times p = 0.1 \times 900 = 90$, and 

standard deviation $= \sqrt{n \times p \times (1 -p)} = \sqrt{900 \times 0.1 \times (1 - 0.1)} = 9$.