assume that the amounts of weight that male college students gain during their freshman year are normally…

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.\na. if 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year.\nthe probability is (square).\n(round to four decimal places as needed.)

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.\na. if 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year.\nthe probability is (square).\n(round to four decimal places as needed.)

Answer

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 $P(-0.24<Z<0.31)=P(Z < 0.31)-P(Z < - 0.24)=0.6217 - 0.4052=0.2165$.

Answer:

$0.2165$