Question

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with mean = 110 grams and standard deviation = 25 grams. What is the probability that a randomly selected vitamin will contain between 82 and 100 grams of pyridoxine?

Answer 1

Answer:

0.21108

Explanation:

Given,

Mean,

$\mu = 110\text{ gram}$

Standard deviation,

$\sigma = 25\text{ gram}$

Let X represents the amount of pyridoxine contained by vitamin,

So, the probability of vitamin will contain between 82 and 100 grams of pyridoxine,

= P( 82 ≤ X ≤ 100 )

$P(\frac{82-\mu}{\sigma}\leq \frac{X-\mu}{\sigma}\leq \frac{100-\mu}{\sigma})$

$P(\frac{82 - 110}{25}\leq z \leq \frac{100-110}{25})$

$P(-1.12\leq z\leq -0.4)$

$P(z\leq -0.4)-P(z\leq -1.12)$

$=0.34458-0.13350$

= 0.21108