Entry to a certain University is determined by a national test. The scores on th
ID: 3232090 • Letter: E
Question
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100.Tom wants to the admitted to this university and he knows that he must better than at least 75% this students who took the test. Tom takes the test and scores 600. Will he be admitted to university? Please step by step show your work. In a shipment of 120 televisions, 6 are defective. If a person buys one television from that shipment, what is the probability that it is not defective? Please step by step show your work, It is claimed that a new treatment is more effective than the standard treatment for prolonging the lives of terminal cancer patients. The standard treatment has been in use for a long time, and from records in medical journals the mean survival period has been 4.1 years with a standard deviation of 1.1 years (standard normal distribution).The new treatment is administered to 64 patients, and their average duration of survival is calculated to be 4.4 years. Write down the null and alternative hypothesis. Is the claim supported by these results? Would you accept or reject the null hypothesis? Please step by step show your work.Explanation / Answer
11a) for 75% ;z score=0.6745
hence corresponding score =mean +z*std deviation =500+100*0.6745=567.45
as his score is better then above ; he should get admission
b)probabilty that it is not defective =114/120 =0.95 (As there are 114 non defective are there among 120)
12) null hypothesis: mean=4.1 years
alternative hypothesis: mean>4.1 years
critical value at 0.05 level z =1.645
std error of mean =std deviation/(n)1/2 =0.1375
for test stat z=(X-mean)/std error =(4.4-4.1)/0.1375=2.1818
as test stat is higher then critical value we reject null hypothesis and conclude that new treatment is more effective
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