Good Morning,

I am trying to work these assignment questions out using R and would greatly appreciate some feedback and/or guidance on if Im calculating these correctly.

Thanks in advance

6. Student marks for a Mathematics course follow a Normal distribution with a mean of 65 marks and a standard deviation of 20 marks. (a). What is the probability that a randomly selected student who follows the Maths course will score between 45 to 60 marks? Answer: If X is N(65, 20) = P(45 # (a) > pnorm(6@, 65, 20) - pnorm(45, 65, 20) [1] 0.2426334 (bl. Calculate the probability that the randomly selected student will fail the cgursg,_ If the pass mark is 49. Answer: If X is N(65, 20) P(X pnorm(49,65,2@) [1] 0.2113554 (c). What should be the cutoff mark for a Higher Distinction (HD) if the facilitator wants only 15% HDs in the offer. Answer: lmnot sure how to calculate this as the following doesn't seem right: > qnorm(@.15, 65, 20) [l] 44.27133 5. A machine is designed to produce bolts with a 3-in diameter. The actual diameter of the bolts has a normal distribution with mean of 3.002 in and standard deviation of 0.002 in. Each bolt is measured and accepted if the length is within 0.005 in of 3 in; otherwise the bolt is scrapped. Find the percentage of bolts that are scrapped. Answer: If x is M1002. 0.002} How does the within 0.005 of 3 in fit into the equation? If I take 0.005 off the 3in does this mean lmtrying to nd the $2.995