Brett discovers that 150 bags of his favorite cookie contain a total of 3750 cookies. He then determines that the cookies in a bag are normally distributed with a standard deviation of 5. When Brett goes to the store to buy a bag of his favorite cookies, how many of the 1200 bags in the store contain more than 30 cookies?
24
25
50
192
600
Does anyone know how to solve this??????
Standard Deviation
This topic has expert replies
Well, first of all, find the mean of 150 bags. 3750 / 150 = 25
Then we know it is a Normal Distribution that has:
1 SD = 68% of the total
2 SD = 95% of the total
3 SD = 99.7% of the total
Our data should be more than 30 cookies, that is more than 1 SD above. Thus, 1 - .68 = .32 = 32%
This 32% contains what is below the mean and what is above the mean, therefore we divide it by 2 to get what is above the mean, ==> .32 / 2 = .16 = 16%
.16 * 1200 = 192 ==> The answer must be [D]
What is the correct answer?
Then we know it is a Normal Distribution that has:
1 SD = 68% of the total
2 SD = 95% of the total
3 SD = 99.7% of the total
Our data should be more than 30 cookies, that is more than 1 SD above. Thus, 1 - .68 = .32 = 32%
This 32% contains what is below the mean and what is above the mean, therefore we divide it by 2 to get what is above the mean, ==> .32 / 2 = .16 = 16%
.16 * 1200 = 192 ==> The answer must be [D]
What is the correct answer?
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You shouldn't need to know that much detail about standard deviation for the GMAT.
Where is this question from?
Where is this question from?
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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