Question

In a shipment of 300 processors, there are 12 defective processors. A quality control consultant randomly collects 6 processors for inspection to determine whether they are defective. Use the Hypergeometric approximation to calculate the following:

a) The probability that there are exactly 2 defectives in the sample

b) The probability that there are at most 5 defectives in the sample, P(X<=5).

## Question 5 Write a script in R to compute the following probabilities of a normal random variable with mean 16 and variance 9

a) lies between 14.4 and 20.3 (inclusive) ```

b) is greater than 21.8 ```

c) is less or equal to 10.5

d) is less than 13 or greater than 19

Answer 1

> #Q5 x~N(16,9)
> #let m=mean and s=standard deiation
> m=16
> s=3
> #a) probabilities lies between 14.4 ad 20.3
> #p(14.4<x<20.3)=p(x<20)-p(x<14.4)
> p=pnorm(20,m,s)-pnorm(14.4,m,s);p
[1] 0.6118874
> #b) probabilities is greater than 21.8
> #p(x>21.8)=1-p(x<21.8)
> p=1-pnorm(21.8,m,s);p
[1] 0.02659757
> #c) probabilities is less than 10.5
> #p(x<10.5)
> p=pnorm(10.5,m,s);p
[1] 0.03337651
> ##b) probabilities is less than 13 or greater than 19
> #p(x<13;x>19)=p(x<13)+p(x>19)
> p=pnorm(13,m,s)+(1-pnorm(19,m,s));p
[1] 0.3173105
>