Question

Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 9 pounds and a standard deviation of 3 pounds. What is the least weight that an individual would have had to lose to be in the top 5% of weight losers?

Answer 1

To find the least weight that an individual would have had to lose to be in the top 5% of weight losers, we need to find the z-score corresponding to the top 5% of the normal distribution.

Step-by-step explanation:

To find the least weight that an individual would have had to lose to be in the top 5% of weight losers, we need to find the z-score corresponding to the top 5% of the normal distribution. We can use the z-score formula:

z = (x - mean) / std_dev

Plugging in the values, we have:

z = (x - 9) / 3

To find the z-score that corresponds to the top 5%, we can use a standard normal distribution table or a calculator. The z-score for the top 5% is approximately 1.645. We can solve for x:

1.645 = (x - 9) / 3

1.645 * 3 = x - 9

4.935 = x - 9

x = 4.935 + 9

x = 13.935

Therefore, the least weight that an individual would have had to lose to be in the top 5% of weight losers is approximately 13.94 pounds.