Question

assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.4 kg and a standard deviation of σ = 4.8 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 the z - scores

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\).
For \(x = 0\), \(z_1=\frac{0 - 1.4}{4.8}=\frac{- 1.4}{4.8}\approx - 0.29\)
For \(x = 3\), \(z_2=\frac{3 - 1.4}{4.8}=\frac{1.6}{4.8}\approx0.33\)

Step2: Use the standard normal distribution table

We want to find \(P(-0.29<Z<0.33)\)
We know that \(P(-0.29 < Z<0.33)=P(Z < 0.33)-P(Z<-0.29)\)
From the standard normal distribution table, \(P(Z < 0.33)=0.6293\) and \(P(Z<-0.29) = 0.3859\)

Step3: Calculate the probability

\(P(-0.29 < Z<0.33)=0.6293-0.3859 = 0.2434\)

Answer:

\(0.2434\)