Question

The average body mass index of children 9 years old is 18.4 with a standard deviation of 4.5. If it is known that the distribution is approximately normal, what is the body mass index of a 9-year-old child at the 82nd percentile

Answer 1

Mass index for a 9-year-old child (at 82nd percentile ) = 22.51

Explanation:

Given:

Mass index for a 9-year-old child = 18.4

Standard deviation = 4.5

Find:

Mass index for a 9-year-old child (at 82nd percentile )

Computation:

At 82nd percentile,

p-value = 0.82

p-value from Z table score = 0.9153

Mass index for a 9-year-old child (at 82nd percentile ) = Mass index for a 9-year-old child + p-value from Z table score(Standard deviation)

Mass index for a 9-year-old child (at 82nd percentile ) = 18.4 + 0.9153(4.5)

Mass index for a 9-year-old child (at 82nd percentile ) = 18.4 + 4.11

Mass index for a 9-year-old child (at 82nd percentile ) = 22.51