## Help with problem for exam, Inference, two sample.

In an effort to enhance the future reaearch performance, the university decided to classify the academic staff based on a RIP mark (Research intelligence potential).
The academic staff will be classified primarily as either lecturers or as researchers
It have been decided if a staff member has a RIP mark less than the CC (classification criterion) he/she willbe classified as an ordanary lecturer but if its higher than the CC the staff member shall be classified as a researcher and receive special treatment.
It may be assumed that the RIP mark for the lecturers is normal distributed with a mean of 120 and a st dev of 10.The RIP mark for researches is assumed to be normal distributed with a mean of 120 and a st dev of 30.

Q1:Given The CC have been specified as 100 determine the probability that a member of the academic staff will be incorrectly identified?

Q2: Determine the value of the Classification criterion, such that the probability that an ordinary lecturer will be incorrectly classified as a researcher is equal to the probability that a "worderful" researcher will be incorrectly classified as a lecturer.

I dont know how to go about the first or the second, bo sample sizes are given.
Is this two populations where i need to determine the sample size and type 2 error?
Or should i combine the two normal distributions to get a normal distribution for the total staff?

Any help would be appreciated

Sorry for the poor spelling and grammar ,

Thank you,