Question

Joyce consumes a mean of 2,000 calories per day with a standard deviation of 130 calories. What is the range within which approximately 95

1) 1,740 to 2,260 calories
2) 1,870 to 2,130 calories
3) 1,940 to 2,060 calories
4) 1,870 to 2,130 calories

Answer 1

The range within which Joyce's caloric intake falls approximately 95% of the time, based on a mean of 2,000 calories and a standard deviation of 130 calories, is 1,740 to 2,260 calories.

Step-by-step explanation:

The question is asking us to determine the range within which approximately 95% of Joyce's daily caloric intake falls based on a given mean and standard deviation. Using the empirical rule for normal distribution, we know that approximately 95% of data falls within two standard deviations from the mean. In this case, the mean is 2,000 calories, and the standard deviation is 130 calories. Therefore, we calculate the range by subtracting and adding two standard deviations (2 x 130) from the mean:

• Lower bound: 2,000 - (2 x 130) = 1,740 calories
• Upper bound: 2,000 + (2 x 130) = 2,260 calories

The range Joyce's caloric intake falls into approximately 95% of the time is 1,740 to 2,260 calories, which corresponds to option 1 in the question provided.