In a random sample of adults aged from 2029 the middle 95 of

In a random sample of adults aged from 20-29, the middle 95% of the men are between168 and 191 cm tall, and the middle 95% of the women are between 155 and 174 cm tall. The heights for each sex follow a normal distribution. Robert and Amanda are each 25 Years. old, and Robert is 12.7 cm taller than Amanda. Which of the following is not a valid pair of z-scores for the couple? Circle your answer. Robert:z=1.0087 Robert:z=0.1739 Amanda:z=-0.7368 Amanda:z=0.8842 Robert:z=0.5565 Robert:z=1.4261 Amanda:z=1.1579 Amanda:z=2.211

Solution

15.

95% of heights lie within 2 standard deviations from the mean.

Thus, for males,

u = 179.5
s = 5.75

For females,

u = 164.5
s = 4.75

Trying, if we do OPTION B, that is,

Robert z = 0.1739

Then his height must be

x(robert) = u + z*s = 179.5+0.1739*5.75 = 180.5

Thus, the height of amanda must be 180.5 - 12.7 = 167.8.

Thus, Amanda\'s z score must be

z(amanda) = (x-u)/s = (167.8-164.5)/4.75 = 0.6947 AND NOT 0.8842.

Hence, that option is not valid. SO the answer is

OPTION B: ROBERT z = 0.1739, Amanda z = 0.8842. [ANSWER]