Question

The total cost for a production process is equal to $1,000 plus two times the number of units produced. The mean and variance for the number of units produced are 500 and 900, respectively. Find the mean and variance of the total cost.

Answer 1

Answer:

$\mu_p=2000\\\\\sigma_p^2=3600$

Step-by-step explanation:

Let X be the number of units produced, and P be the cost of production.

#Given that $\mu_x=500, \sigma_x^2=900$

Cost of production can be calculated as:

$P=1000+2X$

#Mean of the total cost is calculated as;

$\mu_p=1000+2\mu_x\\\\=1000+2(500)\\\\=2000$

Hence, the mean cost of production is $2,000

#Variance of the total cost is calculated as;

$\sigma_p^2=2^2\sigma_x^2\\\\=2^\times 900\\\\=3600$

Hence, the variancecost of production is $3,600