Question

The middle 10% of American men consume between what two weights of sodium? when The average American man consumes 9.5 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.9 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible.

Answer 1

Solution:
Given in the question
Sodium consumption of american men is normally distributed
American man consumes sodium each day ()= 9.5 grams
Standard deviation ()= 0.9 grams
We need to calculate middle 10% of american men consume between what two weights of sodium:
So p-value for lower value = 0.45
p-value for upper value = 0.55
So Z-score from Z table at p-value = 0.45 is -0.1257
Z-score from Z table at p-value = 0.55 is 0.1257
Lower bound for amount of sodium consumed can be calcualted as
X = + Z-score * = 9.5 - 0.1257*0.9 = 9.5 - 0.1131 = 9.3869
Upper bound for amount of sodium consumed can be calcualted as
X = + Z-score * = 9.5 + 0.1257*0.9 = 9.5 + 0.1131 = 9.6131
So middle 10% of american men consume b/w 9.3869 grams and 9.6131 grams weights of sodium.





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