Answer :
Answer:
The variance and standard deviation of X are 0.48 and 0.693 respectively.
The variance and standard deviation of (20 - X) are 0.48 and 0.693 respectively.
Step-by-step explanation:
The variable X is defined as, X = number of defective items in the sample.
In a sample of 20 items there are 4 defective items.
The probability of selecting a defective item is:
[tex]P (X)=\frac{4}{20}=0.20[/tex]
A random sample of n = 3 items are selected at random.
The random variable X follows a Binomial distribution with parameters n = 3 and p = 0.20.
The variance of a Binomial distribution is:
[tex]V(X)=np(1-p)[/tex]
Compute the variance of X as follows:
[tex]V(X)=np(1-p)=3\times0.20\times(1-0.20)=0.48[/tex]
Compute the standard deviation (σ (X)) as follows:
[tex]\sigma (X)=\sqrt{V(X)}=\sqrt{0.48}=0.693[/tex]
Thus, the variance and standard deviation of X are 0.48 and 0.693 respectively.
Now compute the variance of (20 - X) as follows:
[tex]V(20-X)=V(20)+V(X)-2Cov(20,X)=0+0.48-0=0.48[/tex]
Compute the standard deviation of (20 - X) as follows:
[tex]\sigma (20-X)=\sqrt{V(20-X)} =\sqrt{0.48}0.693[/tex]
Thus, the variance and standard deviation of (20 - X) are 0.48 and 0.693 respectively.