reshman et oes this colege have a has an unusually high retention rate? The nati

Question

reshman et oes this colege have a has an unusually high retention rate? The national eshman o sophomore retention rate has held steady at 74%, A certain colege has 493 o the 598 Choose from the following. O A. Yes, because their retention rate is not more than 3 standard deviations above the expected rate of 74%. as sophomores ght to brag that B. ° C. O D. No, because their retention rate is over 4 standard deviations above the expected rate of 74% No, because their retention rate is not more than 3 standard deviations above the expected rate of 74%. Yes, because their retention rate is over 4 standard deviations above the expected rate of 74%

Explanation / Answer

The national retention rate is 74%

and the rate forthe college is

493/598 = 0.8244 , which is 82.44%

which is not very high from 74%

so standard deviation is given as

mean = np = 598*0.74 = 442approx

sd = sqrt(598*0.74*(1-0.74)) = 10.72

so the 4 SD range is

442 +- 4*10.72

399,484

hence as the value 493 falls outside the range hence the correct choice is d

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