Question

Alpha Pharmaceuticals is manufacturing a new antibiotic. The amount of active substance in each pill is normally distributed with a mean of 20 mg and a standard deviation of 2.5 mg. What is the probability of a pill having more than 24.125 mg active substance?

Answer 1

Answer:

The probability of a pill having more than 24.125 mg active substance is 0.0495.

Step-by-step explanation:

Let X denote the amount of active substance in each pill.

It is provided that,$X\sim N(20,\ 2.5^{2})$

Compute the probability of a pill having more than 24.125 mg active substance as follows:

$P(X>24.125)=P(\frac{X-\mu}{\sigma}>\frac{24.125-20}{2.5})$

                       $=P(Z>1.65)\\\\=1-P(Z<1.65)\\\\=1-0.95053\\\\=0.04947\\\\\approx 0.0495$

Thus, the probability of a pill having more than 24.125 mg active substance is 0.0495.