Question

According to the National Vital Statistics, full-term babies' birth weights are Normally distributed with a mean of 7.5 pounds and a standard deviation of 1.1 pounds. What is the probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

Answer 1

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

Explanation:

Problems of normally distributed samples are 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 = 7.5, \sigma = 1.1`

What is the probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

This is the pvalue of Z when X = 8.6 subtracted by the pvalue of Z when X = 6.4. So

X = 8.6

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

`Z = (8.6 - 7.5)/(1.1)`

`Z = 1`

`Z = 1` has a pvalue of 0.8413

X = 6.4

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

`Z = (6.4 - 7.5)/(1.1)`

`Z = -1`

`Z = -1` has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds