4.8 The binomial distribution Quiz

1. $X\sim B(10,0.3)$. Find $\mathrm{Var}(X)$.

• A. $3$
• B. $2.1$
• C. $1.45$
• D. $0.21$

2. Which of these can be modelled by a binomial distribution?

• A. The number of heads in 30 tosses of a fair coin
• B. The number of tosses of a coin until the first head
• C. The time taken to run 100 m
• D. The number of red balls in 3 draws without replacement from a bag of 5 balls

3. $X\sim B(8,0.4)$. Which expression equals $P(X>3)$?

• A. $1-P(X\le3)$
• B. $1-P(X\le4)$
• C. $P(X\le3)$
• D. $1-P(X<3)$

4. $X\sim B(12,0.25)$. Find $P(X=3)$, correct to 3 significant figures.

• A. $0.258$
• B. $0.649$
• C. $0.0156$
• D. $0.391$

5. Each light bulb is faulty with probability $0.02$, independently. What is the least number of bulbs that must be tested so that the probability of finding at least one faulty bulb is greater than 0.5?

• A. $34$
• B. $35$
• C. $25$
• D. $50$