Suppose medical records indicate that the length of newborn babies (in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6. find the probability that a given infant is between 17.4 and 22.6 inches long

Explanation:

1) Find the z-scores:

a) z-score for 22.6 inches length

b) z-score for 17.4 inches length

2) Probability

Then, you have to find the probability that the length of an infant is between - 1.00 and 1.00 standards deviations (σ) from the mean (μ).

That is a well known value of 68%, which is part of the 68-95-99.7 empirical rule.

The most exact result is obtained from tables and is 68.26%:

pie chart because it is in percents ( % )