18+Normal+distributions+when+given+a+percent

Normal distributions when given a percent

The normal distribution is pattern for the distribution of a set of data which follows a bell shaped curve.

The bell shaped curve has several properties:
 * The curve concentrated in the center and decreases on either side. This means that the data has less of a tendency to produce unusually extreme values, compared to some other distributions.
 * The bell shaped curve is symmetric. This tells you that he probability of deviations from the mean are comparable in either direction.

A normal distribution a very important statistical data distribution that is shaped like a bell curve. Normal Distributions are symmetrical with a single peak at the mean of the data. Fifty percent of the distribution lie to the left of the mean and fifty percent lie to the right. The distribution of the data is dependent on the standard deviation. The smaller the standard deviation, the more concentrated the data will be on the data.

Empirical Rule: - 68% of the data lies within one standard deviation of the mean - 95% of the data lies within 2 standard deviations from the mean - 99.7% of the data lies within 3 standard deviations from the mean

IQR (Inter Quartile Range) - The mean containing 50% of the data. - IQR is calculated by subtracting the first quartile from the third quartile

Z-Score Formula Z = z-score x = data point Mean = Mean of Distribution S = Standard Deviation

Using this formula can help us calculate Z - Scores of problems. After applying the formula to the problems, we can find the percentage of the z - score by using the z- score chart below.

1. A school district administered IQ tests to all the students in the district and found the distribution to be normal with a mean of 102 and a standard deviation of 12 A. Find the approximate score of a student that has a score less than 65% of the other students IQ scores.







B. What Are the approximate IQ score for the top 5% of the students?



X=121.8

2. The length of human pregnancies from conception to birth is approximately normal with a mean of 266 days and a standard deviation of 16 days. A. Find the approximate length of a pregnancy that is longer then 40% of other pregnancies.



x = 262

Links ->

http://www.regentsprep.org/Regents/math/algtrig/ATS2/NormalLesson.htm

Z- Score http://www.regentsprep.org/Regents/math/algtrig/ATS7/ZChart.htm

http://mathworld.wolfram.com/NormalDistribution.html