New Zealand
Level 8 - NCEA Level 3

# Binomial Distributions

## Interactive practice questions

Find the value of $\nCr{5}{4}\times\left(0.1\right)^4\times0.9+\nCr{5}{5}\times\left(0.1\right)^5\times\left(0.9\right)^0$5C4×(0.1)4×0.9+5C5×(0.1)5×(0.9)0.

Easy
Approx 2 minutes

Find the value of $\nCr{5}{3}\times\left(0.8\right)^3\times\left(0.2\right)^2+\nCr{5}{4}\times\left(0.8\right)^4\times0.2+\nCr{5}{5}\times\left(0.8\right)^5\times\left(0.2\right)^0$5C3×(0.8)3×(0.2)2+5C4×(0.8)4×0.2+5C5×(0.8)5×(0.2)0.

$X$X is a binomial variable with the probability mass function $P$P$($($X=k$X=k$)$)$=$=$\nCr{5}{k}\times\left(0.7\right)^k\times\left(0.3\right)^{5-k}$5Ck×(0.7)k×(0.3)5k.

$X$X is a binomial variable with a probability distribution given in the table.

### Outcomes

#### S8-4

Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal

#### 91586

Apply probability distributions in solving problems