Question

What weight would give a newborn a z-score of −0.75? grams

Answer 1

Using the normal distribution, it is found that a weight of 3125 grams would given a newborn a z-score of −0.75.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

Researching the problem on the internet, it is found that the mean and the standard deviation for the weight of newborns is given as follows:

$\mu = 3500, \sigma = 500$

Hence, the weight associated with Z = -0.75 is given by X:

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

$-0.75 = \frac{X - 3500}{500}$

X - 3500 = -0.75(500)

X = 3125.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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