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

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

[tex]\mu[/tex] is the mean value

[tex]\sigma[/tex] 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

[tex]P(X>Xo) =1-P(X<Xo)[/tex]

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:

[tex]P(X>34) =1-P(X<34)=1-0.9938=0.0062[/tex]

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

aksnkj aksnkj · Answer 2 · 2021-11-18T07:28:24+01:00

The percentage of students who study 34 hours or more will be 0.0062 or 0.62%.

Given information:

The chemistry 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.

The mean of the data is [tex]\mu=24[/tex].

The standard deviation of the distribution is [tex]\sigma=4[/tex]

It is required to calculate the percentage of students who study 34 hours or more.

So, the value of X will be greater than or equal to 34 ([tex]X\geq 34[/tex]).

Now, we will calculate the probability of students who study 34 hours or more using the normal distribution curve or table.

Use the value of mean as 34, standard deviation as 4, and [tex]X\geq 34[/tex]. Cumulative probability is required to be calculated.

So, from the calculator, the value of the required probability will be,

[tex]P(x\geq 34)=1-P(<34)\\=1-0.99381\\=0.00619\\\approx 0.0062[/tex]

Therefore, the percentage of students who study 34 hours or more will be 0.0062 or 0.62%.

For more details, refer to the link:

https://brainly.com/question/14916937