Question

The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x.

Answer 1

The correct option is (d).

Explanation:

The complete question is:

The random variable x represents the number of computers that families have along with the corresponding probabilities. Use the probability distribution table below to find the mean and standard deviation for the random variable x.

x : 0 1 2 3 4

p (x) : 0.49 0.05 0.32 0.07 0.07

(a) The mean is 1.39 The standard deviation is 0.80

(b) The mean is 1.39 The standard deviation is 0.64

(c)The mean is 1.18 The standard deviation is 0.64

(d) The mean is 1.18 The standard deviation is 1.30

Solution:

The formula to compute the mean is:

`\text{Mean}=\sum x\cdot p(x)`

Compute the mean as follows:

`\text{Mean}=\sum x\cdot p(x)`

`=(0* 0.49)+(1* 0.05)+(2* 0.32)+(3* 0.07)+(4* 0.07)\\\\=0+0.05+0.64+0.21+0.28\\\\=1.18`

The mean of the random variable x is 1.18.

The formula to compute variance is:

`\text{Variance}=E(X^(2))-[E(X)]^(2)`

Compute the value of E (X²) as follows:

`E(X^(2))=\sum x^(2)\cdot p(x)`

`=(0^(2)* 0.49)+(1^(2)* 0.05)+(2^(2)* 0.32)+(3^(2)* 0.07)+(4^(2)* 0.07)\\\\=0+0.05+1.28+0.63+1.12\\\\=3.08`

Compute the variance as follows:

`\text{Variance}=E(X^(2))-[E(X)]^(2)`

`=3.08-(1.18)^(2)\\\\=1.6876`

Then the standard deviation is:

`\text{Standard deviation}=\sqrt{\text{Variance}}`

`=√(1.6876)\\\\=1.2990766\\\\\approx 1.30`

Thus, the mean and standard deviation for the random variable x are 1.18 and 1.30 respectively.

The correct option is (d).