We read: Xfollows the normal distribution (or Xis normally distributed) with mean , and standard deviation ? The normal distribution can be described completely by the two parameters and ? As always, the mean is the center of the distribution and the standard deviation is the measure of the variation around the mean Shape of the normal
• The mean for a distribution of sample proportions is µ pˆ=p, and the standard deviation for a distribution of sample proportions is ? pˆ= pq n • Whenever np ? 10 and nq ? 10, the sampling distribution of a sample proportion can be approximated by a normal distribution (Note that q = 1 - p )
variables with Normal Distributions and the probabilities will correspond to areas under a Normal Curve (or normal density function) This is the most important example of a continuous random variable, because of something called the Central Limit Theorem: given any random variable with any distribution, the average (over many observations) of that
the normal distribution, however, is that it supplies a positive probability density to every value in the range (1 ;+1), although the actual probability of an extreme event will be very low In many cases, it is desired to use the normal distribution to describe the random variation of a quantity that, for physical reasons, must be strictly
Distribution Functions TI-83 & TI-84 Calculators Normal Distribution • Press [2nd] [DISTR] This will get you a menu of probability distributions • Press 2 or arrow down to 2:normalcdf( and press [ENTER] This puts normalcdf( on the home screen Enter the values for the lower x value (x 1), upper x value (x 2), µ, and
Cumulative Standardized Normal Distribution A(z) is the integral of the standardized normal distribution from ??to z (in other words, the area under the curve to the left of z) It gives the probability of a normal random variable not being more than z standard deviations above its mean Values of z of particular importance: z A(z)
distributions → Normal distribution → Plot normal distribution Put in the mean and standard deviation How well does the computer drawing match your sketch?
Students will be able to estimate percentages based on a normal distribution using the make estimates about the U S population that is 65 or older in all other counties and source data online appear at the end of this teacher version