A physician routinely makes physical examinations of children. She is concerned that a three-year-old girl has a height of only 87.8 cm. Heights of three-year-old girls have a mean of 97.5 cm and a standard deviation of 6.9 cm (based on data from the National Health and Nutrition Examination Survey).
a. Use the range rule of thumb to find the maximum and minimum usual heights of three-year-old girls.
b. Based on the result, is the height of 87.8 cm unusual?
c. Should the physician be concerned?
I don't know what your "rule of thumb" is, but:
a. 95% = mean ± 1.96 SD
b. Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
c. If the probability is < .0250 in the smaller portion, the physician might be concerned.
a. The range rule of thumb can be used to estimate the maximum and minimum usual heights for three-year-old girls. According to the rule, the maximum usual height can be estimated by adding two times the standard deviation to the mean, and the minimum usual height can be estimated by subtracting two times the standard deviation from the mean.
Maximum usual height = Mean + (2 * Standard Deviation)
= 97.5 cm + (2 * 6.9 cm)
= 97.5 cm + 13.8 cm
= 111.3 cm
Minimum usual height = Mean - (2 * Standard Deviation)
= 97.5 cm - (2 * 6.9 cm)
= 97.5 cm - 13.8 cm
= 83.7 cm
Therefore, the maximum usual height for three-year-old girls is 111.3 cm, and the minimum usual height is 83.7 cm.
b. To determine if the height of 87.8 cm is unusual, we need to compare it to the usual range. In this case, the usual range of three-year-old girls' heights is between 83.7 cm and 111.3 cm. Since 87.8 cm falls within this range, it can be considered usual.
c. Considering that the height of 87.8 cm falls within the usual range for three-year-old girls, the physician should not be overly concerned based on this measurement alone. However, it may still be important for the physician to monitor the child's growth and development over time to ensure that there are no underlying issues contributing to the lower height.