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I need to figure out how or where to find the standard deviation and mean for this problemGiven 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

Sagot :

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

P ( z≤0 ) = 0.5

P ( z ≤ -3 ) = 0.0013

P ( z ≤ 0 ) -P (z < -3) = 0.5 - 0.0013 = 0.4987

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