Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability.
P(1 ≤ x ≤ 11);
= 3; = 8
Step 1
First, to find areas and probabilities for a random variable x that follows a normal distribution with mean = 3 and standard deviation = 8, we must convert the x values to z values.
Use the formula
z = x − /
to convert the given x values to z values.
Find the z value for x = 1 with mean = 3 and standard deviation = 8.
z = x − /
=
??? − 3 / 8
= ????
Now, find the z value for
x = 11 with mean = 3 and standard deviation = 8.
z = x − /
= ??? − 3 / 8
= ????
Therefore, converted to z values, we wish to find the probability
P _____ ≤ z ≤ _________
The question marks and the blanks need filled in
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