The weight, in grams, of the pair of kidneys in adult males between ages 40 and

Question

The weight, in grams, of the pair of kidneys in adult males between ages 40 and 49 has a bell-shaped distribution with a mean of 325 grams and a standard deviation of 30 grams. Use the empirical rule to determine the following:

a) About 95% of kidney pairs will be between what weights?

b) About 99.7% of kidney pairs will be between what weights?

c) What percentage of kidney pairs weigh more than 415 grams?

d) What percentage of kidney pairs weigh between 295 grams and 385 grams?

e- find any outliers: 36 31 30 31 20 29 24 34 21 28 34

Explanation / Answer

mean = 325 and std. dev. = 30

(A)

As per empirical rule, 95% of normal population lies within 2 sigma levels from the mean.

2*sigma = 2*30 = 60

Hence, 325 - 60 and 325 + 60 = (365, 385) is the weight in grams within which 95% of population lies.

(B)

For 99.7%, 3 Sigma levels are used

3*sigma = 3*30 = 90

325 - 90 = 345 and 325 + 90 = 415

(C)

415 - 325 = 90 grams

P(X > 415) = 1 - 0.997 = 0.003

(D)

325 - 295 = 30 and 385 - 325 = 60

As per empirical rule, 68% of population lies within 1 sigma level.

68% / 2 = 34% and 95% / 2 = 47.5%

Hence 34% + 47.5% = 81.5% of kidney pairs weigh between 295gms and 385 gms

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