Answer to Question #307943 in Statistics and Probability for cassy

Question

the weight of all male senior high school students from one province is measured and is found to be approximately normally distributed with a mean of 115 lbs and standard deviation of 3 lbs. find the percentile rank of the following weights?

A. 112 lbs

B. 115 lbs

Answer 1

Population Mean $(μ) =115$

Population Standard Deviation $(σ) =3$

$Z=\dfrac{X-\mu}{σ} ​$

(a) The percentile rank for 112 lbs

$Z=\dfrac{112-115}{3}$

$Z=-1.0$

From the standard normal distribution tables

$Z(-1.0)=0.15866$

=15.866^th percentile

(b) The percentile rank for 115 lbs

$Z=\dfrac{115-115}{3}$

$Z=0$

From the standard normal distribution tables

$Z(0)=0.50000$

=50^th percentile