Question

The circumference of babies' heads at birth is approximately normal with a mean of 13.39 inches and a standard deviation of 1.75 inches. A clothing manufacturer advertises that its hats for infants are "one size fits all" and can fit any baby with a head circumference between 12.83 and 13.8 inches. What proportion of newborn infants could comfortably wear one of these hats?

Answer 1

To find the proportion of newborn infants that could comfortably wear one of the hats, we need to use the standard normal distribution. By finding the area under the normal curve between the z-scores of the lower and upper limits, we can determine the proportion of newborns that can wear the hats.

Step-by-step explanation:

To find the proportion of newborn infants that could comfortably wear one of the hats, we need to find the proportion of babies' heads that fall within the given range of 12.83 to 13.8 inches.

We can use the standard normal distribution to calculate this. First, we convert the given range to z-scores using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

By finding the area under the normal curve between the z-scores of the lower and upper limits, we can determine the proportion of newborns that can wear the hats.