Question

. diameters of lemons grown on a citrus farm are normally distributed with mean 7 cm and standard deviation 0.5 cm. using the 68-95-99.7 rule, approximately what percentage of lemons have diameters between 7.5 cm and 8 cm? (a) 13.5% (b) 16.0% (c) 2.35% (d) 27.0% (e) 5.0%

Answer 1

To determine the percentage of lemons with diameters between 7.5 cm and 8 cm, we need to find the area under the normal distribution curve between these two values. The percentage is approximately 13.59%, so the answer is 13.5%.

Step-by-step explanation:

To determine the percentage of lemons with diameters between 7.5 cm and 8 cm, we need to find the area under the normal distribution curve between these two values.

First, we need to standardize the values using the formula (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Standardizing 7.5 cm: (7.5 - 7) / 0.5 = 1

Standardizing 8 cm: (8 - 7) / 0.5 = 2

Using a z-table or calculator, we can find the area to the left of 1 and 2. The percentage between these two values is approximately 13.59%. Therefore, the answer is (a) 13.5%.