Question

The serum zinc level (in micrograms per deciliter) for males between ages 15 and 17 has normal distribution with mean 90 and standard deviation 14.

1. If the serum zinc level exceeds 87, what is the probability that it is below 114?

2. Find ? such that 2/3 of males ages 15 and 17 have serum zinc level greater than ?.

Answer 1

µ = 90

σ = 14

If the serum zinc level exceeds 87, what is the probability that it is below 114?

z = (x - µ)/σ

Put x = 87

z = (87 - 90)/14

z = -0.21

P(z > -0.21) = 0.5848

Put x = 114

z = (114 - 90)/14

z = 1.71

P(z < 1.71) = 0.9568

Required probability = 0.9568 - 0.5848 = 0.3719

Find ? such that 2/3 of males ages 15 and 17 have serum zinc level greater than ?.

p-value = 2/3 = 0.67

The z-value for p-value = 0.67 is 0.43.

z = (c - µ)/σ

0.43 = (c - 90)/14

c = 0.43*14 + 90 = 96.03