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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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
hi Bunuel, I have not get clear why you take: 1.5*0.3 did i miss something? Please explain for me
We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.
hi Bunuel, I have not get clear why you take: 1.5*0.3 did i miss something? Please explain for me
We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.
Hope it's clear.
Does the range include specifically numbers 7.65 and 8.55?
hi Bunuel, I have not get clear why you take: 1.5*0.3 did i miss something? Please explain for me
We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.
Hope it's clear.
Does the range include specifically numbers 7.65 and 8.55?
Luckily we don't need to worry about it for this question, though I'd say yes, the range has to be inclusive.
_________________
hi Bunuel, I have not get clear why you take: 1.5*0.3 did i miss something? Please explain for me
We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.
Hope it's clear.
Hello Bunuel, Would you please clear one doubt. The question states that "how many of the 12 listed amounts are within1.5 standard deviation of the mean? In this case, do we need to consider boundary values as well such as (7.65) and (8.55). I mean, If the question had 7.65 value, then would we have considered 7.65 value ? i.e 7.65<= std deviation <= 8.55 is the range Another doubt: If the question had asked Question: how many of the 12 listed amounts are between 1.5 standard deviation of the mean?, and the answer choice had 7.65 as the value
Then, do we need to consider 7.65 value while answering ? I believe, not and 7.65< std deviation < 8.55 will be the range Please provide your comments.
hi Bunuel, I have not get clear why you take: 1.5*0.3 did i miss something? Please explain for me
We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.
Hope it's clear.
Hello Bunuel, Would you please clear one doubt. The question states that "how many of the 12 listed amounts are within1.5 standard deviation of the mean? In this case, do we need to consider boundary values as well such as (7.65) and (8.55). I mean, If the question had 7.65 value, then would we have considered 7.65 value ? i.e 7.65<= std deviation <= 8.55 is the range Another doubt: If the question had asked Question: how many of the 12 listed amounts are between 1.5 standard deviation of the mean?, and the answer choice had 7.65 as the value
Then, do we need to consider 7.65 value while answering ? I believe, not and 7.65< std deviation < 8.55 will be the range Please provide your comments.
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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
A. Four B. Six C. Nine D. Ten E. Eleven
Mean = 8.1 Standard Deviation = 0.3
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.3 = 8.55 and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.3 = 7.65
Except first value 7.51, all other values are within the range hence, 11 values fall within 1.5 SD from Mean
Answer: Option E
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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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
A. Four B. Six C. Nine D. Ten E. Eleven
Mean = 8.1 Standard Deviation = 0.3
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.3 = 8.55 and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.3 = 7.65
Except first value 7.51, all other values are within the range hence, 11 values fall within 1.5 SD from Mean
Answer: Option E
Thanks GMATinsight but why did you have multiply 1.5 with 0.3?
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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
A. Four B. Six C. Nine D. Ten E. Eleven
Mean = 8.1 Standard Deviation = 0.3
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.3 = 8.55 and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.3 = 7.65
Except first value 7.51, all other values are within the range hence, 11 values fall within 1.5 SD from Mean
Answer: Option E
Thanks GMATinsight but why did you have multiply 1.5 with 0.3?
1.5 standard deviation means 1.5*Standard Deviation
i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.3 = 8.55 and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.3 = 7.65
I hope this helps!
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.
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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
A. Four B. Six C. Nine D. Ten E. Eleven
If the Standard Deviation is 0.3 ounces, then 0.3 ounces represents 1 unit of standard deviation. Similarly, 0.6 ounces represents 2 units of standard deviation, 0.15 ounces represents 0.5 units of standard deviation, and so on.
If the mean is 8.1 ounces, then we say that 8.4 ounces is 1 unit of standard deviation above the mean (since 8.1 + 0.3 = 8.4), and we say that 7.8 ounces is 1 unit of standard deviation below the mean (since 8.1 - 0.3 = 7.8)
We want to know how many measurements in the list are within 1.5 standard deviations of the mean
Well, using the above logic, 0.45 represents 1.5 units of standard deviation.
So, 1.5 units of standard deviation below the mean equals 7.65 (8.1 - 0.45 = 7.65) Similarly, 1.5 units of standard deviation abovethe mean equals 8.55 (8.1 + 0.45 = 8.55)
So, any measurement that is between 7.65 ounces and 8.55 will be within 1.5 standard deviations of the mean.
In the given list of measurements, the following meet this requirement:
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 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
A. Four B. Six C. Nine D. Ten E. Eleven
We are given 12 listed amounts of coffee that we can put in order from least to greatest.
We need to determine how many of the listed amounts are within 1.5 standard deviations of the mean. Since the standard deviation is 0.3, 1.5 standard deviations is: 1.5 x 0.3 = 0.45.
1.5 standard deviations above the mean is 8.1 + 0.45 = 8.55
1.5 standard deviations below the mean is 8.1 – 0.45 = 7.65
We see that all the values are between 7.65 and 8.55 except 7.51. Thus, 11 values are within 1.5 standard deviation of the mean.
Re: A vending machine is designed to dispense 8 ounces of coffee
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