Answer to Question #307317 in Statistics and Probability for Niu_bi

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 $(σ) =3$

$Z=\dfrac{X-μ}{σ}$

(a)$Z=\dfrac{112-115}{3}$

$Z=-1.0$

From the standard normal distribution tables

$Z(-1.0)=0.15866$

=15.866^th percentile

(b) $Z=\dfrac{115-115}{3}$

$Z=0$

From the standard normal distribution tables

$Z(0)=0.50000$

=50^th percentile