Percentiles and Normal Distribution Review

6.1-6.3 Normal Distribution review

What have we been doing?

Properties of a Normal Distribution

• Bell-shaped

• Symmetric about the mean

• Area under the curve equals 1

• Group of curves defined by mean and standard deviation

• 68-95-99.7

The STANDARD Normal Distribution

• Special property: mean = 0, standard deviation = 1

Find the area/probability

• given a z-score

• normalcdf calculator command

Multiple Choice

Find the area under the standard normal curve that lies between z=-1.23 and z=1.74.

• -0.8497

• 0.7247

• 0.0684

• 0.8497

Multiple Choice

Find the P(z < 2.10).

• 0.0179

• -0.0179

• 0.9821

• 0.98%

Find a z-score

• given an area

• invnorm calculator command

Multiple Choice

Find the z-score such that the area to the left of the z is 0.3000.

• -1.88

• 0.52

• -0.52

• 1.88

Multiple Choice

Find the z-score such that the area to the right of z is 0.4400.

• -0.15

• -1.71

• 1.71

• 0.15

Multiple Choice

Find the z-score such that the proportion of observations between the mean and the z-score is 0.4898 and z is negative

• z = - 2.32

• z = -0.03

• z = -0.67

• z = -4.99

Multiple Choice

Find the z-score that represents the 80th percentile.

• z=-0.84

• z=1.84

• z=-1.84

• z=0.84

Next Topic . . .

Applications with the Normal Distribution