It is bell-shaped and has a single peak at the center of the distribution. 2. It is symmetrical about the mean 3. It is asymptotic : The curve gets closer and closer to the X -axis but never actually touches it. 4. The location of a normal distribution is determined by the mean, μ , the dispersion or spread of the distribution is determined by the standard deviation, σ . 5. The arithmetic mean , median, and mode are equal 6. The total area under the curve is 1.00 ; half the area under the normal curve is to the right of this center point and the other half to the left of it Different Means and Standard Deviations Equal Means and Different Standard Deviations Different Means and Equal Standard Deviations Family of Distributions LO3 List the characteristics of the normal probability distribution. 7-5
The Standard Normal Probability Distribution n The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. n It is also called the z distribution. n A z- value is the signed distance between a selected value, designated X , and the population mean μ , divided by the population standard deviation, σ . n The formula is: LO4 Convert a normal distribution to the standard normal distribution 7-6
The Normal Distribution – Example The weekly incomes of shift foremen in the glass industry follow the normal probability distribution with a mean of $1,000 and a standard deviation of $100 . What is the z value for the income, let ’ s call it X, of a foreman who earns $1,100 per week? For a foreman who earns $900 per week? LO5 Find the probability that an observation on a normally distributed random variable is between two values. 7-7
Normal Distribution – Finding Probabilities EXAMPLE The mean weekly income of a shift foreman in the glass industry is normally distributed with a mean of $1,000 and a standard deviation of $100. What is the likelihood of selecting a foreman whose weekly income is between $1,000 and $1,100?
- Fall '19