Question

Glaucoma is a disease of the eye that is manifested by high intraocular pressure. The
distribution of intraocular pressure in the general population is approximately normal with
mean 16 mm Hg and standard deviation 3.2 mm Hg. If the normal range for intraocular
pressure is between 10 and 22 mm Hg, than what proportion of the general population would
fall within this range?

Answer 1

A z-table is also known as the standard normal distribution table. The percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.

What is a Z-table?

A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.

Given the mean and the standard deviation are 16mmHg and 3.2 mmHg, therefore, the percentage of the population whose blood pressure will fall in the range of 10 to 22 mm Hg are,

$P(10 < x < 22) = P(\dfrac{10-16}{3.2} < Z < \dfrac{22-16}{3.2})$

$= P(-1.875 < Z < 1.875)\\\\=P(Z < 1.875)-P(Z < -1.875)\\\\= 0.9693-0.0307\\\\= 0.9386$

Hence, the percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.

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