Properties of Normal Distributions 1 The entire family

Properties of Normal Distributions 1 - The entire family of normal distribution is differentiated by its mean µ and its standard deviation σ. 2 - The highest point on the normal curve is at the mean which is also the median and the mode of the distribution. 3 - The mean of the distribution can be any numerical value: negative, zero or positive. 4 - The normal distribution is symmetric 5 - The standard deviation determines how flat and wide the curve is 6 - Probabilities for the random variables are given by areas under the curve. The total area under the curve for the normal distribution is 1 7 - Because the distribution is symmetric, the area under the curve to the left of the mean is 0. 50 and the area under the curve to the right of the mean is 0. 50 8 - The percentage of values in some commonly used intervals are; a-) 68. 3% of the values of a normal r. v are within plus or minus one st. dev. of its mean b-) 95. 4% of the values of a normal r. v are within plus or minus two st. dev. of its mean c-) 99. 7% of the values of a normal r. v are within plus or minus three st. dev. of its mean

Find the area under the standard normal curve that lies 1 - to the right of z = - 0. 55 2 - to the left of z= 0. 84 3 - to the right of z = 1. 69 4 - to the left of z = - 0. 74 5 - between z = 0. 90 and z= 1. 33 6 - between z = -0. 29 and z= 0. 59