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

Answer 2

The total cost mean of the cost of production is $2000 and the variance is $3600.

From the given information, the number of samples (n) is given as 500. Therefore, the total cost will be:

= 1000 + 2n

= 1000 + 2(500)

= 1000 + 1000

= 2000.

Since variance = 900, the standard deviation will be:

= ✓900 = 30

The standard deviation for the total cost will be:

= 2n = 2 × 30 = 60

Variance will be = 60² = 3600

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