Exam 2a Modules 10 to 17

  • Due Oct 18, 2021 at 7:40pm
  • Points 16
  • Questions 32
  • Available Oct 18, 2021 at 6:10pm - Oct 18, 2021 at 7:45pm 1 hour and 35 minutes
  • Time Limit 90 Minutes
  • Allowed Attempts 2

Instructions

Copy the following formulas for use during the exam.  Make sure to scroll down to see all formulas provided.

P(A) + P(Not A) = 1 and P(A) = 1 - P(Not A)

P(A or B) = P(A) + P(B) - P(A and B)

P(A and B) = P(A) x P(B, given A)

P(A and B) = P(A) x P(B) if A and B are independent events

If A and B are independent events, then P(B, given A ) = P(B).  Similarly, P(A, given B) = P(A)

 

Formula for Expected Value is  The mean equals the sum of the values of x times their probabilities.

 

For a normal curve, the Empirical Rule tells us that there is a 68% chance that observations fall within 1 standard deviation of the mean, 95% within 2 standard deviations of the mean, and 99.7% within 3 standard deviations of the mean.

To summarize using probability notation:

  1. LaTeX: P\left(\mu_x-\sigma<X<\mu_x+\sigma\right)=0.68
  2. LaTeX: P\left(\mu_x-2\sigma<X<\mu_x+2\sigma\right)=0.95
  3. LaTeX: P\left(\mu_x-3\sigma<X<\mu_x+3\sigma\right)=0.997

These three facts together are called the empirical rule for normal curves.

For quantitative data:

Z equals open parenthesis x minus mu close parenthesis divided by sigma

 

For categorical data:

LaTeX: standard\:error\:=\:\sqrt{\frac{p\left(1-p\right)}{n}}

LaTeX: Z\:=\:\frac{statistic\:-\:parameter}{standard\:error}=\frac{\hat{p}-p}{standard\:error};     

 LaTeX: Z=\frac{\hat{p}-p}{\sqrt{\frac{p\left(1-p\right)}{n}}}

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