Question

If 25 servings of guacamole have been sold from a batch, in ounces, what is the standard deviation of how much is left? (Suppose the servings of guacamole are independent.)

Answer 1

Answer:

The standard deviation of the the left guacamole is 12.51.

Step-by-step explanation:

As the complete question is not given, thus the complete question is found online and is attached herewith.

From the data

Population mean=$\mu_p$=2.2 ounces

Population Standard Deviation=$\sigma_p$=0.4 ounces

Batch mean=$\mu_b$=80 ounces

Batch Standard Deviation=$\sigma_b$=7 ounces

As per serving is 2.2 ounces

So for 25 servings, Guacamole used is

25*2.2=55 ounces

Thus the Guacamole left is given as

Batch-55=80-55-25 ounces

As it is given that the servings are independent, thus

Var(Z)=Var(X)+Var(Y)

Here Var(Z) is the variance of the Batch, X is the served guacamole and Y is the left guacamole

Also as variance is given as $V=\mu\sigma^2$ so putting the values

$Var(Z)=Var(X)+Var(Y)\\\mu_b\sigma_b^2=\mu_s\sigma_s^2+\mu_l\sigma_l^2\\80.7^2=55(0.4)^2+25*\sigma_l^2\\\sigma_l^2=3911.2/25\\\sigma_l^2=156.448\\\sigma_l=12.51$

So the standard deviation of the the left guacamole is 12.51.