Question

assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean $mu = 1.3$ kg and a standard deviation of $sigma = 5.5$ 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 (square).
(round to four decimal places as needed.)

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$. For $x = 0$, $z_1=\frac{0 - 1.3}{5.5}=\frac{- 1.3}{5.5}\approx - 0.24$. For $x = 3$, $z_2=\frac{3 - 1.3}{5.5}=\frac{1.7}{5.5}\approx0.31$.

Step2: Find probabilities from z - table

We use the standard normal distribution table. The probability corresponding to $z_1=-0.24$ is $P(Z < - 0.24)=0.4052$. The probability corresponding to $z_2 = 0.31$ is $P(Z < 0.31)=0.6217$.

Step3: Calculate the required probability

The probability that a student gains between 0 kg and 3 kg is $P(-0.24

Answer:

$0.2165$