Question

assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.2 kg and a standard deviation of σ = 5.7 kg. complete parts (a) through (c) below.
a. if 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. the probability is
(round to four decimal places as needed.)

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set.
For $x = 0$, $z_1=\frac{0 - 1.2}{5.7}=\frac{- 1.2}{5.7}\approx - 0.21$
For $x = 3$, $z_2=\frac{3 - 1.2}{5.7}=\frac{1.8}{5.7}\approx0.32$

Step2: Find probabilities from z - table

We want to find $P(0Using the standard normal distribution table, $P(Z < 0.32)=0.6255$ and $P(Z<-0.21) = 0.4168$.
Then $P(-0.21

Answer:

$0.2087$