Question

"The weight of a product is normally distributed with a mean of four ounces and a variance of .25 squared ounces. What is the probability that a randomly selected unit from a recently manufactured batch weighs no more than 3.5 ounces?

Answer 1

Explanation:

Since the weight of the products are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = weight of the product.

µ = mean weight

σ = standard deviation

From the information given,

µ = 4 ounces

Variance = 0.25²

σ = √variance = √0.25² = 0.25

We want to find the probability that a randomly selected unit from a recently manufactured batch weighs no more than 3.5 ounces. It is expressed as

P(x ≤ 3.5)

For x = 3.5,

z = (3.5 - 4)/0.25 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.0228