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# z-area probability question Watch

1. A normal distribution has a mean of 4.20 and a standard deviation of 1.00. use z-area probability tables to find the probability of obtaining a value between 3.70 and 5.81.
Explain your working using sketches of relevant probability areas, and give your answer to 3 decimal places.
2. Hi

You require: P( 3.70 < X < 5.81)

To find your z values use: z = (x - mean)/ standard deviation

Then, sketch a bell shaped (norm. dist or pdf) curve with mean '0' and variance '1' squared

Plot the z equivalent of 5.81 (which will be to positive therefore to the right of the '0' mean) and 3.70 (which will be negative therefore to the left of the '0' mean) extending vertical lines from each z value on the base axis up to the curve and shade the area between the two.

Using symmetry, you will discover that this is the equivalent of P(z < 5.81 z value) - (1 - P( z < than the positive 3.70 z value))

Hope this helps.

Jonty

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Updated: April 2, 2013
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