Question

According to the WHO report, girls who are one month old have a mean head circumference of 36.55 centimeters with a standard deviation of 1.17 cm.

1) Ann is concerned that her daughter’s head is small. Her daughter has a head circumference of 34.25 centimeters when she is one-month old. If we consider measurements more than 2 standard deviations from the mean as unusual, is Ann’s daughter’s head measurement unusually small? Support your answer.
2) According to Medscape.com, microcephaly is a head circumference more than two standard deviations below the mean. What percentage of 1-month old girls will be categorized as having microcephaly? How do you know?

Answer 1

Ann's daughter's head measurement is unusually small as it falls more than 2 standard deviations away from the mean. Approximately 2.28% of 1-month old girls will be categorized as having microcephaly.

Step-by-step explanation:

The question asks whether Ann's daughter's head measurement of 34.25 centimeters at one month old is unusually small. To determine this, we need to calculate the z-score, which measures how many standard deviations away a value is from the mean.

The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation. For Ann's daughter, the z-score is (-1.82). Since this value is more than 2 standard deviations away from the mean, Ann's daughter's head measurement can be considered unusually small.

According to the definition of microcephaly given by Medscape.com, a head circumference more than two standard deviations below the mean is categorized as microcephaly. To find the percentage of 1-month old girls with microcephaly, we can use the properties of the standard normal distribution.

Approximately 2.28% of the data falls more than 2 standard deviations below the mean. Therefore, around 2.28% of 1-month old girls will be categorized as having microcephaly.