For a standard normal distribution, determine the following probabilities a) P(z

Question

For a standard normal distribution, determine the following probabilities a) P(z > 1.47 b) b) P (z > -0.32) c) P(-1.66 lessthanorequalto z lessthanorequalto -0.64) d) P (-1 65 lessthanorequalto z lessthanorequalto 0.21) a) P(z > 1.47) = (Round to four decimal places as needed.) b) (P > z -0.32) = (Round to four decimal places as needed.) c) P(-1.66 lessthanorequalto z lessthanorequalto -0.64) = (Round to four decimal places as needed.) d) P (-1 65 lessthanorequalto z lessthanorequalto 0.21) = (Round to four decimal places as needed.)

Explanation / Answer

a)

p(z>1.47) = 1 - p( z < 1.47)

= 1 - 0.92922

= 0.0708

b)

p(z> - 0.32) = p(z<0.32)

= 0.6255

c)

p(-1.66 <= z <= -64) = p(z<=-0.64) - p(z<= -1.66)

= [ 1 - p(z<=0.64)] - [1 - p(z<=1.66)]

= [1-0.73891] - [ 1-0.95154]

= 0.2611-0.0485

= 0.2126

d)

p (-1.65<=z<=0.21) = p(z<=0.21) - p(z <= -1.65)

= 0.58317 - (1-p(z<=1.65)

= 0.58317 - [ 1- 0.95035]

= 0.5335

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