# Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5. Find the probability that a value is greater than or equal to 75. please show work

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embizze | Certified Educator

Given `mu=70,sigma=4.5` in a normal distribution, find the probability that a value is greater than or equal to 75.

Convert 75 to a normal z-score using `z=(x-mu)/sigma`

`z=(75-70)/4.5=10/9=1.11`

We want to find `P(x>=75)` ;

`P(x>=75)=P(z>=1.11)`

From a standard normal table we find that the probability of a z-value greater than 1.11 is .1335 (Most tables give the probability/area to the left of the given z-score -- in that case subtract the .8665 from the table from 1 to get the answer.)

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The probability of a random value being greater than or equal to 75 is approximately 13.4%

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