A national study reported that 75% of high school graduatespursue a college educ

Question

A national study reported that 75% of high school graduatespursue a college education immediately after graduation. A privatehigh school advertises that 158 of their 186 graduates last yearwnt on to college. Does this school have an unusually highproportion of students going to college? I found the standard deviation to be 3.13, but was wonderingwhich one of the two conclusions would be correct. A) This school cannot boast that an unusually high proportionof their students go on to college. Their proportion is only 3.13standard deviations above the mean. B) This school can boast that an unusually high proportion oftheir students go on to college. Their proportion is 3.13 standarddeviations above the mean. A national study reported that 75% of high school graduatespursue a college education immediately after graduation. A privatehigh school advertises that 158 of their 186 graduates last yearwnt on to college. Does this school have an unusually highproportion of students going to college? I found the standard deviation to be 3.13, but was wonderingwhich one of the two conclusions would be correct. A) This school cannot boast that an unusually high proportionof their students go on to college. Their proportion is only 3.13standard deviations above the mean. B) This school can boast that an unusually high proportion oftheir students go on to college. Their proportion is 3.13 standarddeviations above the mean.

Explanation / Answer

The probability of that standard deviation or higher occuring isnormcdf(3.13,10000000000)=.000874, which is .087%. This is so low that I would go withoption B)This school can boast that an unusuallyhigh proportion of their students go on to college. Theirproportion is 3.13 standard deviations above themean.

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