Question

A drug company believes that the annual demand for a drug will follow a normal random variable with a mean of 900 pounds and a standard deviation of 60 pounds. if the company produces 1000 pounds of the drug, what is the chance (rounded to the nearest hundredth ) that it will run out of the drug? assume that the only way to meet the dertand for the drug is to use this year's production number.

Answer 1

Following the z-score formula, z = (X - μ) / σ, we can calculate z = (1000-900)/60 = 1.67
Using the z-table

we can see that the z-score of 1.67 corresponds to a probability of .9525. The probability that we run out of the drug

Answer 2

Answer:

The chance that it will run out of the drug is 0.95.

Step-by-step explanation:

Given : A drug company believes that the annual demand for a drug will follow a normal random variable with a mean of 900 pounds and a standard deviation of 60 pounds. if the company produces 1000 pounds of the drug.

To find : What is the chance that it will run out of the drug?

Solution :

Applying z-score formula,

$z=\frac{x-\mu}{\sigma}$

Where, x is the sample mean x=1000

$\mu=900$ is the population mean

$\sigma=60$ is the standard deviation.

Substitute the value in the formula,

$z=\frac{1000-900}{60}$

$z=\frac{100}{60}$

$z=1.67$

Using the z-table,

The value at z=1.67 is X=0.9525

Therefore, The chance that it will run out of the drug is 0.95.