a.Let z be a random variable with a standard normal distribution. Find the indic

Question

a.Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
P(z 1.22)

b. Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(2.04 z 0.44)

c.Find z such that 5.3% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)

d.Find z such that 96.5% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)

Explanation / Answer

Solution:-
a) P(z 1.22) = 0.1112

b) P(2.04 z 0.44) = (1-0.3299) - 0.0207 = 0.6494

c) P(z < z) = 0.053

As this is less than 50%, z must be negative.
so, P(z < -z) = P(z > z) => 1 - P(z < z)
i.e. 1 - 0.053 = 0.947
z = -1.62

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