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A data set has arithmetic mean of 35 and standard deviation of 4 , whi
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13 Jul 2025, 23:29
13 Jul 2025, 23:29
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Question Stats:
66% (00:32) correct
33% (00:19) wrong based on 3 sessions
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A data set has arithmetic mean of 35 and standard deviation of 4 , which of the following values is/ are more than 1.5 standard deviation from the mean?
Indicate all that apply
\(\boxed{A} 24\)
\(\boxed{B} 28\)
\(\boxed{C} 32\)
\(\boxed{D} 40\)
\(\boxed{E} 42\)
\(\boxed{F} 44\)
Indicate all that apply
\(\boxed{A} 24\)
\(\boxed{B} 28\)
\(\boxed{C} 32\)
\(\boxed{D} 40\)
\(\boxed{E} 42\)
\(\boxed{F} 44\)
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Official Answer
A,B,E,F
Re: A data set has arithmetic mean of 35 and standard deviation of 4 , whi
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20 Jul 2025, 08:50
20 Jul 2025, 08:50
Expert Reply
To determine which values are more than 1.5 standard deviations from the mean, we first need to calculate the boundaries for this range.
Given:
- Arithmetic mean $\((\mu)=35\)$
- Standard deviation $\((\sigma)=4\)$
First, calculate the value of 1.5 standard deviations:
$$
\(1.5 \times \sigma=1.5 \times 4=6\)
$$
Now, calculate the lower and upper bounds for values that are within 1.5 standard deviations of the mean:
- Lower Bound: $\(\mu-1.5 \sigma=35-6=29\)$
- Upper Bound: $\(\mu+1.5 \sigma=35+6=41\)$
A value is more than $\(\mathbf{1 . 5}\)$ standard deviations from the mean if it is either:
- Less than 29
- OR
- Greater than 41
Now, let's check each of the given options against these criteria:
- (A) 24: Is $\(24<29\)$ ? Yes.
- (B) 28: Is $\(28<29\)$ ? Yes.
- (C) 32: Is $\(32<29\)$ ? No. Is $\(32>41\)$ ? No.
- (D) 40 : Is $\(40<29\)$ ? No. Is $\(40>41\)$ ? No.
- (E) 42: Is $\(42<29\)$ ? No. Is $\(42>41\)$ ? Yes.
- (F) 44: Is $\(44<29\)$ ? No. Is $\(44>41\)$ ? Yes.
The values that are more than 1.5 standard deviations from the mean are $\(24,28,42\)$, and \(44\) .
The final answer is $\(\mathrm{A}, \mathrm{B}, \mathrm{E}, \mathrm{F}\)$.
Given:
- Arithmetic mean $\((\mu)=35\)$
- Standard deviation $\((\sigma)=4\)$
First, calculate the value of 1.5 standard deviations:
$$
\(1.5 \times \sigma=1.5 \times 4=6\)
$$
Now, calculate the lower and upper bounds for values that are within 1.5 standard deviations of the mean:
- Lower Bound: $\(\mu-1.5 \sigma=35-6=29\)$
- Upper Bound: $\(\mu+1.5 \sigma=35+6=41\)$
A value is more than $\(\mathbf{1 . 5}\)$ standard deviations from the mean if it is either:
- Less than 29
- OR
- Greater than 41
Now, let's check each of the given options against these criteria:
- (A) 24: Is $\(24<29\)$ ? Yes.
- (B) 28: Is $\(28<29\)$ ? Yes.
- (C) 32: Is $\(32<29\)$ ? No. Is $\(32>41\)$ ? No.
- (D) 40 : Is $\(40<29\)$ ? No. Is $\(40>41\)$ ? No.
- (E) 42: Is $\(42<29\)$ ? No. Is $\(42>41\)$ ? Yes.
- (F) 44: Is $\(44<29\)$ ? No. Is $\(44>41\)$ ? Yes.
The values that are more than 1.5 standard deviations from the mean are $\(24,28,42\)$, and \(44\) .
The final answer is $\(\mathrm{A}, \mathrm{B}, \mathrm{E}, \mathrm{F}\)$.
gmatclubot
Re: A data set has arithmetic mean of 35 and standard deviation of 4 , whi [#permalink]
20 Jul 2025, 08:50
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