Question

The weight of a product is normally distributed with a mean of 4 ounces and a variance of .25 squared ounces. What is the probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces

Answer 1

Answer: 0.0228

Step-by-step explanation:

Let x be the weight of a product.

The probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces:

$P(X>5)\\\\=P(\dfrac{X-Mean}{\sqrt{Variance}}>\dfrac{5-4}{\sqrt{0.25}})\\\\=P(Z>\dfrac{1}{0.5}) \ \ \ [z=\dfrac{X-Mean}{\sqrt{Variance}}]\\\\=P(z>2)\\\\=1-P(Z$

Hence, the required probability = 0.0228