Question

assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of $mu = 1.1$ kg and a standard deviation of $sigma = 4.6$ 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 \(x = 0\), \(z_1=\frac{0 - 1.1}{4.6}\approx - 0.24\)
For \(x = 3\), \(z_2=\frac{3 - 1.1}{4.6}\approx0.41\)

Step2: Find the probabilities using the standard normal distribution table

We know that \(P(0<X<3)=P(-0.24<Z<0.41)\)
\(P(-0.24 < Z < 0.41)=P(Z < 0.41)-P(Z<-0.24)\)
From the standard normal table, \(P(Z < 0.41)=0.6591\), \(P(Z<-0.24)=0.4052\)

Step3: Calculate the final probability

\(P(-0.24 < Z < 0.41)=0.6591-0.4052 = 0.2539\)

Answer:

\(0.2539\)