Question

The Z-score is based on the concept of the normal distribution, the fact that we can expect 95% of the values in the distribution to be between 2 standard deviations below the average and 2 standard deviations above the average. Say the average weight of a 4 year old girl is 15 kilograms and the standard deviation is 3 kilograms.

What is true of the following weights:
12 kilograms
a) maybe not healthy
b) definitely not healthy
c) in perfect health
d) We can say nothing based on this

Answer 1

C.) In perfect health.

Explanation:

Given an average weight of 15kg and a standard deviation of 3kg for children of 4 years. Since the weight is based on a normal Z - distribution of 95% which is mean ± 2(standard deviations)

Mean weight interval is :

15 - 2(3) ; 15 + 2(3)

(9 ; 21) ; this weight interval could be interpreted to mean the normal or perfect weight value.

Therefore, given that the child weighs 12kg

Since, 12 kg falls within in the interval, we can conclude that the child is in perfect health.