Normal Probability Distributions Normal Probability Plots

Density Curve What does the curve measure? Density Curve: An idealized description of the overall pattern of a distribution. Area underneath = 1, representing 100% of observations.

Density Curves Density Curves come in many different shapes; symmetric, skewed, uniform, etc. The area of a region of a density curve represents the % of observations that fall in that region. The median of a density curve cuts the area in half. The mean of a density curve is its “balance point.”

What is a Normal curve? A normal curve is but not Since both curves are symmetrical, what can you say about their means and medians? Notation: N( ,  ) –  (mu) the mean of a density curve –  (sigma) standard deviation of a density curve How would you write the distribution of women’s heights with a mean of 64.5 and standard deviation of 2.5? How would you write the distribution of men’s heights with a mean of 69 and standard deviation of 2.5?

 What is the area between -1  and -1  ? What is the area between -2  and -2  ? What is the area between -3  and -3  ?

What if the z-score is not exactly 1, 2, or 3? Computing the Standard Normal variable z  (mu) the mean of a density curve  (sigma) standard deviation of a density curve

 Find P(z < 1.85) 1.85 From Table A:.9678

 Find P(z > 1.85) 1.85 From Table A: =.0322

 Find P(z < -.79) -.79 From Table A:.2148

 Find P( -.79 < z < 1.85) -.79 = P(z < 1.85) - P(z < -.79) =.7530

 Find P( -.3 < z < 1.6) = P(z < ___) - P(z < _____)

Length of Pregnancies The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. Sketch and shade an appropriate Normal distribution. What percent of pregnancies last less than 245 days? What percent of pregnancies last between 245 and 281 days? How long do the longest 30% of the pregnancies last?

Normal Distributions, Percentiles and Quartiles Where is the 10 th percentile of a Normal distribution? Where is the 90 th percentile of a Normal distribution? What are the quartiles of a Normal distribution?

Normal Probability Plot

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