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?

Free Course Hero Answer

Course Hero Answer & Explanation:

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=σxμ

to find P(x > 8)

first, convert x = 8 to z-value

z=σxμ

z=0.58−8​

z = 0

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

Screen Shot 2021-08-28 at 9.58.31 AM.png

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

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