I need to figure out how or where to find

Randy Dean

Randy Dean

Answered question

2022-02-11

I need to figure out how or where to find the standard deviation and mean for this problem Given that z is a standard normal random variable, compute the following probabilities.
a. P(z≤−1.0)
b. P(z≥−1)
c. P(z≥−1.5)
d. P(−2.5≤z)
e. P(−3

Answer & Explanation

iluvyou23452nwj

iluvyou23452nwj

Beginner2022-02-12Added 19 answers

a. P(z≤−1.0)
Using the z - score table, that gives the probabilities to the left side of the z score:
P ( z ≤−1.0) = 0.1587
b. P(z≥−1)
1 - P ( z ≤−1.0) = 1 - 0.1587 = 0.8413
c. P(z≥−1.5)
1 - P(z≤−1.5) = 1 -0.0668 = 0.9332
d. P(−2.5≤z)
P (z ≥ -2.5)
1 - P (z ≤-2.5) = 1 - 0.0062 = 0.9938
e. P(−3<z≤0)
P ( z≤0 ) = 0.5
P ( z > -3 ) = 1 - P ( z ≤ -3 ) = 1 - 0.0013 = 0.9987
P ( z ≤ 0 ) -P (z < -3) = 0.5 - 0.0013 = 0.4987

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