Question

THIS IS EXAM REVIEW, so please make sure to show the work and make sure the work is correct.

In all tests of hypothesis use the 5% level of significance unless told otherwise. In all confidence interval problems use 95% confidence unless told otherwise. SHOW YOUR WORK.

2. Test scores for a mathematics course have a normal distribution with a mean of 76 and a standard deviation of 12.

a.What proportion of scores will be between 70 and 90?

b. The instructor wants to give A's to the top 15% of her class. What score would a student need to get an A?

Answer 1

This can be done using statcrunch calculator. I am not sure whether you use the same calculator or not but I hope the work shown below makes sense. May be you can implement that on your calculator if you use some different one or otherwise I would suggest you to mention the calculator as well, (if specific).

a. Given mean = 76, standard deviation = 12 and the distribution is normal

Use the normal statcrunch calculator, plug the values of mean and standard deviation as shown. Select the "between" option from top and put 70 < X < 90 to get the proportion of students between 70 and 90. It is equal to 0.5698

b. To get A, student need to be in top 15% means the remaining student proportion is 85% who will not get A.

Now, select the "standard" option from top and with same mean and standard deviation, Now, put 0.85 in right hand side box to get the cutoff score which is 88.44. Means a student must score 88.44 or above to get among top 15% and get an A grade from her teacher.