A statistics instructor designed an exam so that the grades would be roughly normally distributed with a mean of and a standard deviation of 1015. In the space provided, draw a sketch of this distribution and label the mean and, using the standard deviation, two additional points on the horizontal axis. (2 pts)

a) Figure attached

b)

And we can find this probability with the normal standard table and with the complement rule:

Step-by-step explanation:

A statistics instructor designed an exam so that the grades would be roughly normally distributed with a mean of μ=75 and a standard deviation of σ= 10.

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Figure attached.

Part b

What proportion of students are expected to earn grades of ≥90?

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability with the normal standard table and with the complement rule:

seems like d

step-by-step explanation: