Multiple Choice
Sketch a graph to represent the probability, then use a calculator to find it.
6. Normal Distribution & Continuous Random Variables
Probabilities & Z-Scores w/ Graphing Calculator
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Use a calculator to find the z–scores of the region shown in the standard normal distribution below.
A = 0.800
A
B
C
D
Verified step by step guidance1
Start by understanding that the problem involves finding the z-scores that correspond to a central area of 0.800 under the standard normal distribution curve.
Sketch a standard normal distribution curve, which is symmetric around the mean (0). The area under the curve between two z-scores is given as 0.800.
Recognize that the total area under the standard normal curve is 1. Therefore, the area in the tails (outside the central 0.800 area) is 1 - 0.800 = 0.200.
Since the distribution is symmetric, divide the tail area by 2 to find the area in each tail: 0.200 / 2 = 0.100. This means each tail has an area of 0.100.
Use a standard normal distribution table or calculator to find the z-scores that correspond to the cumulative area of 0.100 in each tail. These z-scores will be approximately -1.28 and 1.28, as they represent the points where the cumulative area from the left is 0.100 and 0.900, respectively.
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