Calorie Intake Probability Calculation

A research study was conducted to determine the daily calorie intake of a sample of individuals from three different age groups: 18-30, 31-50, and 51-70. The mean daily calorie intake for each age group is as follows:

• 18-30 years: 2,500 calories
• 31-50 years: 2,200 calories
• 51-70 years: 1,900 calories

During the study, it was noted that the daily intake for individuals in the 18-30 age group had a standard deviation of 300 calories, while those in the 31-50 age group had a standard deviation of 350 calories. The 51-70 age group demonstrated a standard deviation of 250 calories. If the calorie intake of a random individual from the 31-50 age group is chosen at random, what is the probability that their intake will be below 1,800 calories? Assume that calorie intakes are normally distributed.

Use the mean and the standard deviation of this age group to calculate the z-score and then find the corresponding probability from the standard normal distribution.