Module 10 Module Quiz Extension 1

Module 10 Quiz

15 multiple choice questions covering the binomial distribution: Bernoulli trials, binomial probabilities, mean and variance, cumulative probabilities, and the normal approximation.

Module 10 Quiz

Q11 MARK

A random variable $X$ has distribution $\text{Bin}(n, p)$. What does $n$ represent?

AThe probability of success BThe number of failures only CThe number of independent trials DThe expected value

Q21 MARK

For a binomial random variable $X \sim \text{Bin}(n, p)$, $P(X = x)$ equals

A$x/n$ B$p^{x}(1 - p)^{n - x}$ C$^{n}P_{x}\, p^{x}$ D$\binom{n}{x} p^{x}(1 - p)^{n - x}$

Q31 MARK

Which condition is required for a binomial model?

AThe probability of success changes each trial BThe trials are dependent CThe number of trials is unknown DThere are two outcomes on each trial

Q41 MARK

If $X \sim \text{Bin}(10, 0.3)$, then $E(X)$ is

A$0.3$ B$0.7$ C$3$ D$7$

Q51 MARK

If $X \sim \text{Bin}(12, 0.25)$, then $\text{Var}(X)$ is

A$3$ B$2.25$ C$0.1875$ D$9$

Q61 MARK

For $X \sim \text{Bin}(5, 0.4)$, $P(X = 0)$ is

A$0.4^{5}$ B$1 - 0.6^{5}$ C$0.6^{5}$ D$5(0.4)(0.6)^{4}$

Q71 MARK

For $X \sim \text{Bin}(8, p)$, $P(X \le 2)$ means

A$P(X = 2)$ only B$P(X > 2)$ C$P(X = 3) + ... + P(X = 8)$ D$P(X = 0) + P(X = 1) + P(X = 2)$

Q81 MARK

If $X \sim \text{Bin}(n, p)$, the standard deviation is

A$\sqrt{np(1 - p)}$ B$np$ C$\sqrt{n}$ D$np(1 - p)$

Q91 MARK

Expected frequency in a sample of size $N$ is found by

Adividing the probability by $N$ B$N$ multiplied by the relevant probability Cusing $n - p$ Dignoring the sample size

Q101 MARK

Which expression gives $P(X \text{ at least } 1)$?

A$P(X \le 0)$ B$1 - P(X = 0)$ C$P(X = 0)$ D$P(X = 1)$ only

Q111 MARK

When using the normal approximation to a binomial distribution, a continuity correction is used because

Aa discrete distribution is being approximated by a continuous one Bthe normal has only integer values Cthe mean is zero Dthe binomial is continuous

Q121 MARK

For $X \sim \text{Bin}(20, 0.5)$, the distribution is

Asymmetric about $10$ Balways skewed right Cnot defined Dalways skewed left

Q131 MARK

A Bernoulli trial is

Aa trial with infinitely many outcomes Ba single trial with success or failure Ca continuous measurement Da trial whose probability changes after every attempt

Q141 MARK

If $X \sim \text{Bin}(6, 0.2)$, which expression represents $P(X = 2)$?

A$\binom{6}{2}(0.2)^{4}(0.8)^{2}$ B$\binom{6}{2}(0.2)^{2}(0.8)^{4}$ C$\binom{2}{6}(0.2)^{2}(0.8)^{4}$ D$6(0.2)^{2}$

Q151 MARK

The mode of a binomial distribution is usually near

A$p/n$ B$n/p$ C$1 - p$ D$(n + 1)p$