Question

The weight at birth of males has a mean value of 3.53 kg with a standard deviation of 0.58. What birth weight has a​ z-score of​ 0.81?

Answer 1

A birth weight of 3.9998kg has a z-score of 0.81.

Explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 3.53, \sigma = 0.58`

What birth weight has a​ z-score of​ 0.81?

This is X when Z = 0.81. So:

`Z = (X - \mu)/(\sigma)`

`0.81 = (X - 3.53)/(0.58)`

`X - 3.53 = 0.58*0.81`

`Z = 3.9998`

A birth weight of 3.9998kg has a z-score of 0.81.