Question

A study investigated about 3000 meals ordered from Chipotle restaurants using the online site Grubhub. Researchers calculated the sodium content (in milligrams) for each order based on Chipotle’s published nutrition information. The distribution of sodium content is approximately Normal with mean 2000 mg and standard deviation 500 mg.

About what percent of the meals ordered exceeded the recommended daily allowance of 2400 mg of sodium?

20.00%
21.20%
42.40%
80.00%
78.80%

Answer 1

Approximately 21.20% of the meals ordered from Chipotle via Grubhub exceeded the recommended daily allowance of 2400 mg of sodium. Therefore correct option is B

Step-by-step explanation:

We need to calculate the percentage of meals that exceeded 2400 mg of sodium. Given that the distribution of sodium content is approximately Normal with a mean of 2000 mg and standard deviation of 500 mg, we can use the standard normal distribution (Z-scores) to find this percentage.

First, we calculate the Z-score for 2400 mg of sodium:

1. Z = (X - μ) / σ
2. Z = (2400 - 2000) / 500
3. Z = 400 / 500
4. Z = 0.8

Now, we look up the Z-score of 0.8 in the standard normal distribution table (or use a calculator) to find the proportion of values to the left of 2400 mg, which gives us approximately 0.7881 or 78.81%.

To find the proportion to the right (which are the meals exceeding 2400 mg), we subtract this value from 1 (or 100%):

1 - 0.7881 = 0.2119 or 21.19%

Therefore, approximately 21.20% of the meals ordered from Chipotle via Grubhub exceeded the recommended daily allowance of 2400 mg of sodium.