The heights of children 2 years old are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. pediatrician regularly measure the heights of toddlers to determine whether there is a problem. pediatrician determines that there may be a problem when a child is in the top or bottom of 5% heights. what is the height of a 2 year old that could be a problem

The problematic heights are those lower than 29.5325 inches and higher than higher than 34.4675 inches

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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:

Pediatrician determines that there may be a problem when a child is in the top or bottom of 5% heights.

Bottom 5%

Any height lower than the value of X when Z has a pvalue of 0.05. So

A height lower than 29.5325 inches is problematic.

Top 5%

Any height higher than the value of X when Z has a pvalue of 0.95. So

A height higher than 34.4675 inches is problematic.

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490