Question

the term \freshman 15\ refers to the claim that college students typically gain 15 lb during their freshman year at college. assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of 2.9 lb and a standard deviation of 10.7 lb. find the probability that a randomly selected male college student gains 15 lb or more during his freshman year. what does the result suggest about the claim of the \freshman 15\?
the percentage of freshmen that gain 15 pounds or more in their first year of university is
(round to one decimal place as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x = 15\) (the value we are interested in), \(\mu=2.9\) (the mean), and \(\sigma = 10.7\) (the standard deviation).

$$z=\frac{15 - 2.9}{10.7}=\frac{12.1}{10.7}\approx1.13$$

Step2: Find the probability using the standard normal distribution

We want to find \(P(X\geq15)\), which is equivalent to \(P(Z\geq1.13)\) (since \(X\) is normally distributed).
Using the property \(P(Z\geq z)=1 - P(Z < z)\).
From the standard - normal table, \(P(Z < 1.13)=0.8708\)

$$P(Z\geq1.13)=1 - 0.8708 = 0.1292$$

Answer:

\(12.9\%\)