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

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

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((X-\mu)/(\sigma)>(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.