Let z be a standard normal random variable with a mean of 0 and a standard...

Let z be a standard normal random variable with a mean of 0 and a standard devi- ation of 1. Find the following probabilities:

(a) P(−0.5<z<0.5) (b) P(−.5<z<1.5)

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Expert Solution

Let z be a standard normal random variable with a mean of 0 and a standard deviation of 1.

Q.1) We want to find, the following probabilities,

a) P(-0.5 < z < 0.5)

= 2 * P(Z < 0.5) - 1

= 2 * 0.6915 - 1

= 1.3830 - 1

= 0.3830

=> P(-0.5 < z < 0.5) = 0.3830

b) P(-0.5 < z < 1.5)

= P(Z < 1.5) - P(Z < -0.5)

= 0.9332 - 0.3085

= 0.6247

=> P(-0.5 < z < 1.5) = 0.6247

c) P(-1.5 < z < -0.75)

= P(Z < -0.75) - P(Z < -1.5)

= 0.2266 - 0.0668

= 0.1598

=> P(-1.5 < z < -0.75) = 0.1598

d) P(2 < z < 3)

= P(Z < 3) - P(Z < 2)

= 0.9987 - 0.9332

= 0.0215

=> P(2 < z < 3) = 0.0215

orchestra answered 1 year ago

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