Question

An organization measures child development by comparing the weights of children who are the same height and the same gender. In a certain year, weights for all 80 cm girls in the reference population had a mean (Greek letter Mu) = 10.6 kg and a standard deviation (Greek letter Sigma) = 0.8 kg. Weights are normally distributed. X~N(10.6, 0.8). Calculate the z-scores that correspond to the following weights and interpret them. (Round your numerical answers to two decimal places.) (a) 11.4 kg, z=__. A child who weighs 11.4 kg is__standard deviation(s) above or below the mean of 10.6 kg. (b) 8.3 kg z =__. A child who weighs 8.3 kg is__standard deviation(s) above or below the mean of 10.6 kg. (c) 12.6 kg z=__. A child who weighs 12.6 kg is__standard deviation(s) above or below the mean of 10.6 kg.

Answer 1

Solution:

Given:  Weights are normally distributed. X~N(10.6, 0.8).

That is:
u= 10.6
kg and
8'0 = 0
kg.

Calculate the z-scores that correspond to the following weights and interpret them.

Part a) x = 11.4 kg,

z score formula is:

1 -

0.8 11.4 - 10.6 0,8 8 = 1.00

z = 1.00

Interpretation:

A child who weighs 11.4 kg is 1.00 standard deviation above the mean of 10.6 kg.

Part b) 8.3 kg

z value is:

18.3 - 10.6 108 -2.3 -=-2.875 = -2.88 08

z = -2.88

Interpretation:

A child who weighs 8.3 kg is 2.88 standard deviation below the mean of 10.6 kg.

Part c) 12.6 kg

z value is:

| 12.6 - 10.6 08 2.0 -2.50

z = 2.50

Interpretation:

A child who weighs 12.6 kg is 2.50 standard deviation above the mean of 10.6 kg.