Question

PLEASE ANSWER IN R SCRIPT

In a shipment of 20 engines, history shows that the probability of any one engine proving unsatisfactory is 0.1

a) Use the Binomial approximation to calculate the probability that at least three engines are defective?
```{r}
#INSERT YOUR ANSWER HERE
```

b) Use the Poisson approximation to calculate the probability that at least three engines are defective?
```{r}
#INSERT YOUR ANSWER HERE
```

c) Compare the results of parts a and b, then illustrate on how well the Poisson probability distribution approximates the Binomial probability distribution.
```{r}
#INSERT YOUR ANSWER HERE
```

Answer 1

a)

here this is binomial with parameter n=20 and p=0.1

below is R scrpit:

> 1-pbinom(2,20,0.1)
[1] 0.3230732

b)

expected number of defects =np=20*0.1 =2

> 1-ppois(2,2)
[1] 0.3233236

c)

here since probability from two distribution are very close, Poisson probability distribution approximates the Binomial probability distribution very well