Question

Suppose that total carbohydrate intake in 12- to 14-year-old boys is normally distributed, with mean = 124 g/1000 cal and standard deviation = 20 g/1000 cal. What percentage of boys in this age range have carbohydrate intake above 140 g/1000 cal?

Answer 1

By calculating the z-score for 140 g/1000 cal and using the standard normal distribution, approximately 21.19% of boys aged 12 to 14 have a carbohydrate intake above that amount.

Step-by-step explanation:

To calculate the percentage of 12- to 14-year-old boys who have a carbohydrate intake above 140 g/1000 cal, we can use the normal distribution with a mean (μ) of 124 g/1000 cal and a standard deviation (σ) of 20 g/1000 cal. We first need to find the z-score, which represents the number of standard deviations from the mean.

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value of interest. In this case, X = 140 g/1000 cal.

So, the z-score is (140 - 124) / 20 = 0.8.

After finding the z-score, we can use a standard normal distribution table or a calculator to find the corresponding percentile. The table value for z = 0.8 is approximately 0.7881, which means that about 78.81% of the population falls below 140 g/1000 cal. Therefore, to find the percentage above 140 g/1000 cal, we subtract this value from 1 (or 100%).

1 - 0.7881 ≈ 0.2119 or 21.19%.

Thus, approximately 21.19% of boys in this age range have a carbohydrate intake above 140 g/1000 cal.