Student take an average of 45 minutes and standard deviation of 8 minutes to complete a certain statistics test. If a student is selected at random, what is the probability that the student takes more than 56 minutes to compete the test?

To solve this problem, we can use the z-score formula and the standard normal distribution.

The formula for the z-score is given by:

�=�−��

z=σ

X−μ

where:

�

X is the individual data point (in this case, the time taken by a student),

�

μ is the mean,

�

σ is the standard deviation.

For this problem:

�=45

μ=45 minutes (mean),

�=8

σ=8 minutes (standard deviation),

�=56

X=56 minutes (time taken by a student).

Calculate the z-score:

�=56−458

z=8

56−45

�≈1.375

z≈1.375

Now, we need to find the probability that a randomly selected student takes more than 56 minutes. This corresponds to finding the area to the right of �=1.375

z=1.375 in the standard normal distribution.

You can use a standard normal distribution table or a calculator to find this probability. Many calculators and statistical software provide the functionality to find the cumulative probability for a given z-score.

Using a standard normal distribution table or calculator, find the probability corresponding to �=1.375

z=1.375 or the area to the right of �=1.375

z=1.375. The result will give you the probability that a randomly selected student takes more than 56 minutes to complete the test.