Question

Height and weight are two measurements used to track a child's development. The World Health Organization measureschild development by comparing the weights of children who are the same height and the same gender. In 2009, weightsfor all 80 cm girls in the reference population had a mean u = 10.2 kg and standard deviation 0 = 0.8 kg. Weights arenormally distributed. X ~ N(10.2, 0.8). Calculate the z-scores that correspond to the following weights and interpret them.a. 11 kgb. 7.9 kgc 122 kg

Answer 1

Answer with explanation:

Let x be the random variable that represents the weights of all 80 cm girls.

Given : $\mu=10.2\ kg\ \ ; \ \sigma=0.8\ kg$

 

Formula to calculate z-score :

$z=\dfrac{x-\mu}{\sigma}$

a) Z-score for x= 11 kg

$z=\dfrac{11-10.2}{0.8}=1$

i.e. z=1

Interpretation : A child who weighs 11 kg is 1 standard deviations above the mean weight 10.2 kg.

b) Z-score for x= 7.9 kg

$z=\dfrac{7.9-10.2}{0.8}=-2.875$

i.e. z=-2.875

Interpretation : A child who weighs 11 kg is 2.875 standard deviation deviation below the mean weight 10.2 kg.

c) Z-score for x= 12.2 kg

$z=\dfrac{12.2-10.2}{0.8}=2.5$

i.e. z=2.5

Interpretation : A child who weighs 11 kg is 2.5 standard deviations above the mean weight 10.2 kg.

Answer 2

The z-scores that correspond to the following weights 11 kg, 7.9 kg, 12.2 kg are 1, -2.875 and 2.5 respectively.

What is z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

Given that:

Mean = 10.2 kg, standard deviation = 0.8 kg,

For 11 kg:

z = (11 - 10.2) / 0.8 = 1

For 7.9 kg:

z = (7.9 - 10.2) / 0.8 = -2.875

For 12.2 kg:

z = (12.2 - 10.2) / 0.8 = 2.5

The z-scores that correspond to the following weights 11 kg, 7.9 kg, 12.2 kg are 1, -2.875 and 2.5 respectively.

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