the annual per capita consumption of fresh oranges in pounds in the united states can be approximated by a normal distribution, with a mean of 9.9 pounds and a standard deviation of 2.5 pounds. what largest annual per capita consumption of oranges that can be in the bottom 5% of consumption?
You can play around with Z table stuff here:
http://davidmlane.com/hyperstat/z_table.html
To find the largest annual per capita consumption of oranges that can be in the bottom 5% of consumption, we need to determine the cutoff point or the threshold value.
Given that the annual per capita consumption of fresh oranges follows a normal distribution with a mean (μ) of 9.9 pounds and a standard deviation (σ) of 2.5 pounds, we can use the standard normal distribution table or z-score calculations to find the threshold value.
Step 1: Calculate the z-score corresponding to the bottom 5% of consumption.
We can look up the z-score from the standard normal distribution table or use an online calculator.
The z-score corresponding to a cumulative probability of 0.05 (5%) is approximately -1.645.
Step 2: Use the z-score to find the threshold value (X) for the annual per capita consumption.
We can use the formula:
X = μ + (z * σ)
Given:
μ (mean) = 9.9 pounds
σ (standard deviation) = 2.5 pounds
z = -1.645
Plugging in the values:
X = 9.9 + (-1.645 * 2.5)
X = 9.9 - 4.1125
X ≈ 5.7875
Therefore, the largest annual per capita consumption of oranges that can be in the bottom 5% is approximately 5.79 pounds.