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 longer than 20 inches.

Step-by-step

The normal probability curve is symmetrical about the mean.  

This means that for an event that is normally distributed, there is a 50% probability that it falls below the mean, and a 50% probability that it falls above.

From the given information, the mean is 20" and we need the probability that a given infant is longer than 20", namely the mean.

Therefore by the definition of the normal probability curve, there is a 50% probability that the length falls above 20".

This can be verified by referencing a normal probability table with Z=0, meaning at the mean, the probability is equal to 0.5 for Z<0, and therefore 0.5 for Z>0.

Z=(X-mean) / Standard deviation

When Z>0, X (measurement) is greater than the mean

When Z<0, X is less than the mean.