请教PREP数学题

gheyete

A vending machine is designed to dispense 8 ounces of coffee into a cup.
After a test that recorded the number of ounces of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data.
If the 1,000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?



(A) Four

(B) Six

(C) Nine

(D) Ten

(E) Eleven

答案为E

For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean.
What was the mean score for the examination?



(A) 74

(B) 76

(C) 78

(D) 80

(E) 82

答案为A

我觉得只要遇到这类似的题我就不会做，望各位給我讲解讲解。。不甚感激！

Knightll

LZ，第一题是有图的吗？否则没有办法做。

2. 设mean=m, std deviation=d, 有等式 58+2d=m 和 98-3d=m --> d=8, m=74
58 was 2 std deviation below the mean: 意思是58比平均值要少2个std deviation； 同理，98 was 3 std deviation above the mean: 意思是98比平均值要多3个std deviation

希望可以帮到LZ

gheyete

非常感谢。。

bensealet

据多方考证，Prep里录入这个题的时候没有把那12个数字写出来。所以有了那12个samples的具体值之后就很好做了 你看题目描述有个“ the 12 listed amounts”  
用8.1加减1.5X0.3 之后得出区间值，把那12个数字带进去就知道符合条件的有11个