Question

In a random sample of 1149 men aged 35–44, the mean total cholesterol level was 212 mg/dl with a standard deviation of 38.7 mg/dl. If total cholesterol levels are normally distributed, what is the highest total cholesterol level a man in this age range can have and still be in the bottom 5%? Round your answer to the nearest hundredth.

The annual per capita consumption of apples in the U.S. is approximately normally distributed with μ=17.1 lb and σ=4.2 lb. What annual consumption amount is the tenth percentile? Round your answer to the nearest hundredth.

The weights of boxes of a certain breakfast cereal are approximately normally distributed with a mean weight of 24 oz and a standard deviation of 0.08 oz. The lightest 5% of boxes do not meet minimum weight requirements and must be repackaged. To the nearest hundredth of an ounce, what is the minimum weight requirement for a cereal box?  oz

Jerzy has drawn certain conclusions from his database of 65,597 scores on a certain test. To check the robustness of his conclusions, he decides to recompute his statistics after discarding the top and bottom 10% of the scores. If the scores are normally distributed with mean 72 and standard deviation 10.7, what are the lowest and highest scores he will keep? (All the scores are positive integers.)

      Low score:      High score:

Answer 1

Solution:-

1) The highest total cholesterol level a man in this age range can have and still be in the bottom 5% is 148.34.

Mean = 212, S.D = 38.7

p-value for the bottom 5% = 0.05

z-score for the p-value = - 1.645

By applying normal distribution:-

x = 148.34

2) The annual consumption amount at the tenth percentile is 11.72.

Mean = 17.1, S.D = 4.2

p-value for the 10th percentile = 0.10

z-score for the p-value = - 1.282

By applying normal distribution:-

x = 11.7156