prep关于标准差的一题 求助！谢谢

adamilan

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?


7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53



(A) Four

(B) Six

(C) Nine

(D) Ten

(E) Eleven

adamilan

求助！在线等 谢谢！

ivyfangwei

mean=8.1 standard deviation=0.3
算出正负1.5方差的区间 [8.1-0.3*1.5,8.1+0.3*1.5]=>[7.65, 8.55]=11个？

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?


7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53



(A) Four

(B) Six

(C) Nine

(D) Ten

(E) Eleven

-- by 会员 adamilan (2012/5/5 21:51:52)

adamilan

想请问为什么要0.3*1.5？谢谢！

mean=8.1 standard deviation=0.3
算出正负1.5方差的区间 [8.1-0.3*1.5,8.1+0.3*1.5]=>[7.65, 8.55]=11个？

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?


7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53



(A) Four

(B) Six

(C) Nine

(D) Ten

(E) Eleven

-- by 会员 adamilan (2012/5/5 21:51:52)

-- by 会员 ivyfangwei (2012/5/5 22:02:27)

ivyfangwei

我也做错过类似的题目的，看解析是这么算的，就记住了。真心不好意思，说不出道道来，惭愧。。。话说答案是11个么？

adamilan

是11个 对的 没事儿 谢谢啦 我找不到这题的解析啊

我也做错过类似的题目的，看解析是这么算的，就记住了。真心不好意思，说不出道道来，惭愧。。。话说答案是11个么？

-- by 会员 ivyfangwei (2012/5/5 22:08:43)

ivyfangwei

The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television.  The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours.  The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean.  Which of the following could be the number of hours that Pat watched television last week?

(A) 30
(B) 20
(C) 18
(D) 12
(E) 6
答案D

Average(mean) for the town = 21 h
Standard deviation for the town = 6 h

Pat was between 1 and 2 standard deviations below the mean.

One standard deviation below the mean = Mean - 1*SD = 21 - 6 = 15 h

Two standard deviations below the mean = Mean - 2*SD = 21 - 2(6) = 21 - 12 = 9 h

Therefore, the correct answer (the numbers of hours Pat watched television) lies between 9 and 15 h.

The only correct answer that satisfies that condition is D (12 h).

你可以看看这道我之前做错的题，解释附上

adamilan

非常感谢!!

The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television.  The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours.  The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean.  Which of the following could be the number of hours that Pat watched television last week?

(A) 30
(B) 20
(C) 18
(D) 12
(E) 6
答案D

Average(mean) for the town = 21 h
Standard deviation for the town = 6 h

Pat was between 1 and 2 standard deviations below the mean.

One standard deviation below the mean = Mean - 1*SD = 21 - 6 = 15 h

Two standard deviations below the mean = Mean - 2*SD = 21 - 2(6) = 21 - 12 = 9 h

Therefore, the correct answer (the numbers of hours Pat watched television) lies between 9 and 15 h.

The only correct answer that satisfies that condition is D (12 h).

你可以看看这道我之前做错的题，解释附上

-- by 会员 ivyfangwei (2012/5/5 22:18:36)