Question

Your friend is about to begin an introductory chemistry course at his university. The course has collected data from students on their study habits for many years, and the professor reports that study times (in hours) for the final exam closely follow a normal distribution with mean 24 and standard deviation 4. What percentage of students study 34 hours or more

Answer 1

Answer:

The percentage of students sudy 34 hours or more is 0.62%

Step-by-step explanation:

The Normal Distribution

The bell curve or normal distribution is frequently used to model the probability of natural random events. The normal distribution $N(\mu,\sigma)$ is characterized by two parameters:

$\mu$ is the mean value

$\sigma$ is the standard deviation

The study times in hours for the final exam is modeled as a normal distribution N(24,4). We are required to find the percentage of students study 34 hours or more, or P(X>34).

The values for the cumulative probability are given by tables or digital means like Excel where we can get the left-tail or P(X<Xo). To compute the right-tail or P(X>Xo) we use this relation

$P(X>Xo) =1-P(X$

The Excel formula to find the left-tail cumulative probability is called

NORM.DIST(x,mean,standard_dev,cumulative)

To solve the question, we used:

NORM.DIST(34,24,4,TRUE)=0.9938

Thus:

$P(X>34) =1-P(X$

The percentage of students study 34 hours or more is 0.62%