Question

8. Biometric Security In designing a security system based on eye (iris) recognition, we must

consider the standing eye heights of women, which are normally distributed with a mean of

59.7 in. and a standard deviation of 2.5 in.

(Source: based on anthropometric survey data from Gordon, Churchill, et al.)

a. If an eye recognition security system is positioned at a height that is uncomfortable for women

with standing eye heights less than 54 in., what percentage of women will find that height

uncomfortable?

b. In positioning the eye recognition security system, we want it to be suitable for the lowest 95% of

standing eye heights of women. What standing eye height of women separates the lowest 95% of

standing eye heights from the highest 5%?

Answer 1

8)

Solution :

Given that ,

mean = = 59.7

standard deviation = = 2.5

(a)

P(x < 54) = P[(x - ) / < (54 - 59.7) / 2.5]

= P(z < -2.28)

= 0.0113

Answer = 1.13%

(b)

P(Z < 1.645) = 0.95

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 2.5 + 59.7 = 63.8

height = 63.8 in