Algebra II : Probability

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #7 : Mean, Standard Deviation, And Normal Distribution

In a normal distribution, what percentage is covered within one standard deviation?

Possible Answers:

99.7%

34%

95%

50%

68%

Correct answer:

68%

Explanation:

By drawing a bell curve, the middle line is 50%. One standard deviation left and right of the middle line is 34% each. That means one standard deviation within is 68%

Example Question #8 : Mean, Standard Deviation, And Normal Distribution

If the mean is \(\displaystyle \small 0\) and the standard deviation is \(\displaystyle \small 3.4\), which of the following is NOT within two standard deviations?

Possible Answers:

\(\displaystyle \small \small -6.81\)

\(\displaystyle \small -6.79\)

\(\displaystyle \small -6.8\)

\(\displaystyle \small 6.79\)

\(\displaystyle \small 6.80\)

Correct answer:

\(\displaystyle \small \small -6.81\)

Explanation:

Two standard deviations means to double the standard deviation value.

\(\displaystyle 2\cdot 3.4 =6.8\)

This means the range is \(\displaystyle \small -6.8\) to \(\displaystyle \small 6.8\)

\(\displaystyle (0-6.8, 0+6.8)\rightarrow (-6.8,6.8)\)

Only \(\displaystyle \small -6.81\) is not in the range. 

Example Question #9 : Mean, Standard Deviation, And Normal Distribution

Ibram was paid $5000 for editing a 2200-page encyclopedia. What was his rate earned per page?

Possible Answers:

$0.44

$2.27

$1.27

$0.56

Correct answer:

$2.27

Explanation:

This question is really just asking for the average dollar per page. This could be easily calculated:

\(\displaystyle \frac{5000}{2200}=2.27\)

However, you might also think of this as a rate problem:

D=RT

Using the information from the question, we can see that D=5000 and T=2200.

This comes out to what we solved above:

\(\displaystyle R=\frac{D}{T}=\frac{5000}{2200}=2.27\)

Example Question #5 : Mean, Standard Deviation, And Normal Distribution

Standard Deviation can be calculated from what statistical term?

Possible Answers:

Quartile

Mode

Range

Median

Variance

Correct answer:

Variance

Explanation:

Another way to calculate standard deviation is the square root of variance.

Variance is,

 \(\displaystyle \small {\frac{\Sigma (x-\bar{x})^2}{n-1}}\).  

Taking the square root of this is how standard deviation can be calculated. 

\(\displaystyle \sigma=\sqrt{\small {\frac{\Sigma (x-\bar{x})^2}{n-1}}}\)

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