Question: The weight of oranges growing in an orchard is normally distributed with a mean weight of 8oz. and a standard deviation of 0.5 oz. What is the probability that a randomly selected Orange from the orchard weighs more than 8 oz., to the nearest thousandth? -Free Course Hero Question Answer.

Question Description: The weight of oranges growing in an orchard is normally distributed with a mean weight of 8oz. and a standard deviation of 0.5 oz. What is the probability that a randomly selected Orange from the orchard weighs more than 8 oz., to the nearest thousandth?

This means the probability that a randomly selected orange from the orchard weighs more than 9 oz is 0.5Step-by-step explanation

Given:

μ = 8 oz

σ = 0.5 oz

Using the conversion of z -score to solve for x

z=σx−μ​

to find P(x > 8)

first, convert x = 8 to z-value

z=σx−μ​

z=0.58−8​

z = 0

0 is located in the center of the distribution, the shaded part is to the right of 0

since the probability from the center to the left end tail of the distribution is 0.5 as well the probability from the center to the right end tail of the distribution is 0.5

This means the probability that a randomly selected orange from the orchard weighs more than 9 oz is 0.5