Final answer:
Using the standard normal distribution, we find that 67% of values fall below the z-score of approximately 0.44. Multiplying this by the standard deviation (15 mg) and adding it to the mean (200 mg) gives us C = 206.6 mg, which, when rounded to the nearest option, suggests an answer of C = 215 milligrams.
Step-by-step explanation:
The question requires finding the value of C where 67% of the cholesterol content in large chicken eggs is less than C. This implies that we need to find the z-score that corresponds to the 67th percentile in the normal distribution since the cholesterol content is normally distributed. Using the standard normal distribution table, we find that the closest percentile to 67% is approximately at a z-score of 0.44. To find the actual cholesterol content value, we use the formula:
C = μ + z • σ
Where μ is the mean, σ is the standard deviation, and z is the z-score. Given that μ (mean cholesterol) is 200 milligrams and σ (standard deviation) is 15 milligrams, we calculate:
C = 200 + 0.44 • 15
C = 200 + 6.6
C = 206.6 milligrams
Since this is not an option in the multiple choices and our calculated value is very close to B) 215 milligrams, we can round up our value to the nearest option to determine that B) 215 milligrams is the most likely answer.