Download Precalculus – Chapter 3: Section 3-1

Notes:







Hmwk
Precalculus – Chapter 13: Statistics and Probability
Section 13-5: Normal Distributions (Page 889)
Normal Curve – bell curve
Normal distributions – used to predict the outcomes of many events
o Used to predict if an outcome is statistically significant or just
by chance
o Symmetric about the mean
o X-axis is a horizontal asymptote
o Area under the curve is 1
o The maximum is at the mean
o Has two points of inflection (at 1 standard deviation to the right
and to the left of the mean)
o Mean, median, and mode are all the same value (the center), μ
Standard Normal Curve – mean of 0 and a standard deviation of 1
o Parent function for all normal curves
o Change in μ  horizontal translation
o Change in σ  horizontal stretch and vertical compression or
vice versa
–(x- μ)2
Equation of a Normal Curve: y = 1
e 2σ2
σ √(2π)
Empirical Rule:
o 68% within 1 σ
o 95% within 2 σ
o 99.7% within 3 σ
Standardize – make it match a standard normal distribution
Z-value – number of standard deviations that a data value is above
the mean
o Z = (x – μ) / σ
where x is the data point, μ is the mean, and σ
is the standard deviation
o Area under a normal curve between x = a and x = b is equal to
the are under the standard normal curve between the z-value of
a and the z-value of b
 Page 896: 1 – 29 odd