Question

The weights of oranges are normally distributed with a mean of 12.4 pounds and a standard deviation of 3 pounds. Find the minimum value that would be included in the top 10% of orange weights. Use a TI-83, TI-83 plus, or TI-84 calculator, and round your answer to one decimal place.

Answer 1

16.24 pounds

Explanation:

First, find the z-score for the 90th percentile (top 10%). You can use the z-table or a calculator. In this case, you're looking for the z-score such that 90% of the data falls below it, which corresponds to a z-score of 1.28 approximately. You can use the calculator to find this value as well.Now, use the z-score formula to find the corresponding weight value:

X = μ + (Z * σ)

Where X is the value you're looking for. μ is the mean (12.4 pounds). Z is the z-score (1.28).σ is the standard deviation (3 pounds).X = 12.4 + (1.28 * 3)

Calculate the value

X ≈ 12.4 + 3.84 ≈ 16.24 pounds.

So, the minimum value that would be included in the top 10% of orange weights is approximately 16.2 pounds when rounded to one decimal place.