Arianna G.

asked • 03/17/23

Please help me solve this

For a standard normal distribution, find:


P(z > c) = 0.0135


Find c rounded to two decimal places.



Marla G.

tutor
Your told it's a standard normal distribution, so that means z has this distribution: N(0,1), in other words, you know the mean & standard deviation of Z. The formula for z is.: z = (x-μ)/σ. Or, you can also look in the standard normal (i.e. z table) to see what value of z has a probability=0.0135. Just check to make sure the table is reporting the probability that z is > some value(c), and not < some value (c) !
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04/06/23

1 Expert Answer

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Nathaniel Z. answered • 06/13/24

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Ph.D. Candidate in Economics with 4+ Years Teaching Experience

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If you draw a normal distribution curve, you are looking for the x value where 1.35% of the data is to the right of this x. Depending on what resources you have available there are two approaches you can take to solve this question.


  1. First 1 - 0.0135 = 0.9865. Then, if you have a normal distribution table, look for this value and figure out which row and column you are in to determine the value of c. We do not directly look for the value 0.0135 as normal distribution tables provide the probability of being to the left of a given point, and we are interested in being to the right of the point.
  2. If you have a graphing calculator or software tool, you should have an inverse normal function. On a TI-84 it is called invNorm. Plug in the value 0.9865 and keep the mean as 0 and standard deviation as 1.

Either way, you should get c = 2.21 (approximately).

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