Question

If the distribution of weight of newborn babies in Maryland is normally distributed with a mean of 3.89 kilograms and a standard deviation of 0.68 kilograms, find the weights that correspond to the following Z-scores. Round your answers to the nearest tenth, if necessary. (a) z = -1.35 kilograms (b) z = 2.64 kilograms

Answer 1

Answer:

a) 3 kilograms

b) 5.7 kilograms

Step-by-step explanation:

Z-score:

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

$Z = \frac{X - \mu}{\sigma}$

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 question:

$\mu = 3.89, \sigma = 0.68$

We have to find X for both values of Z.

a) z = -1.35

$Z = \frac{X - \mu}{\sigma}$

$-1.35 = \frac{X - 3.89}{0.68}$

$X - 3.89 = -1.35*0.68$

$X = 3$

3 kilograms

b) z = 2.64

$Z = \frac{X - \mu}{\sigma}$

$2.64 = \frac{X - 3.89}{0.68}$

$X - 3.89 = 2.64*0.68$

$X = 5.7$

5.7 kilograms