Standard Deviation Problems

[freezer]

• There are these 8 numbers in a set 9.4,9.9,9.9,9.9,10.0,10.2,10.2,10.5 The mean and standard deviation of the 8 numbers are 10.0 and 0.3 respectively, what percent of the 8 numbers are within 1 standard deviation of the mean?
  a) 90%
  b) 85%
  c) 80%
  d) 75%
  e) 70%

Need a detailed solution: Thanks

[krishna_k1]

1 standard deviation in this case is 9.7 to 10.3 six numbers are within this range so the answer is 6/8 * 100 = 75%

[aru4912]

Agree; three 9.9's ,10.0 & two 10.2's are within 1 SD of the mean (10.0) => 6/8 * 100 = 75%

[karta]

Can anyone please explain the solution above in detail. What does 1 standard deviation mean ?

[jsackmann]

The question says "The mean and standard deviation of the 8 numbers are 10.0 and 0.3 respectively" so:

mean = 10
sd = 0.3

"one standard deviation" = 1*(sd) = 0.3.

two standard deviations would be 2*(sd) = 0.6, etc.

A number that is within SD away from the mean could be greater or less than the mean -- in this case, it could be either of the following:

greater than 10 - 0.3 = 9.7
less than 10 + 0.3 = 10.3

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[sharma1617]

The fourth grade at school X is made up of 300 students who have a total weight of 21,600 pounds.
If the weight of these four graders has a normal distribution and standard deviation equals 12 pounds, approximately what percentage of the fourth graders weighs more than 84 pounds?

a 12%
b 16%
c 36%
d 48%
e 60%

need detailed explanation,,and also want to know what are bell curve questions and how it will relate with standard deviaion. thanks

[ramgorur]

here μ = 72
μ + 1.σ = 72 + 12 = 84



% of students above 84 = 13.6% + 2.1% + 0.1% = 14.8% ≈ 15%

[matt01752]

Where did you get this question? My believe is that GMAT will not be asking questions like this....

Mean = 21600/300 = 72

Mean + 1sigma (std dev) = 72 + 12 = 84

+/- 1<sigma> covers 68.2% (34.1% + 34.1%) of the normal distribution. Therefore, remain distribution of data 100% - 68.2% = 31.8%.

Since we care only about data points above 84 lbs => 31.8 / 2 = 15.9% = 16%

What's the answer?

+Matt

[sharma1617]

This question is not from GMAT preparation. This is from cracking the GRE from princeton review. Since i got stuck by this question that why asked it, and yes the correct answer is 16%

[sharma1617]

PERMUTATION AND COMBINATION

A teacher prepares a test. She gives 5 objective type question out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choice and last 3 have 4 choice.

help me with this question,,is there any specific formula applied in thes type of questions???