Question

For each probability expression, find the unknown zz-value(s). Unless directed otherwise, use three decimals in your answers.

(a) P(−1.6≤Z≤1.06)=P(−1.6≤Z≤1.06)=

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(b) P(Z≥z0)=0.3P(Z≥z0)=0.3. Find z0z0.

z0=z0=

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(c) P(z0≤Z≤0.73)=0.6272P(z0≤Z≤0.73)=0.6272. Find z0z0.

z0=z0=

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(use two decimals

Answer 1

Solution:

a)

P(-1.6 < z < 1.06)

= P(z < 1.06) - P(z < -1.6)

= 0.8554 - 0.0548 Using standard normal table,  

Probability = 0.801

b)

P( Z z0 ) = 0.3

1 - P( Z < z0 ) = 0.3

P( Z < z0 ) = 1 - 0.3

P( Z < z0 ) = 0.7

P( Z < 0.524) = 0.7

z0 = 0.524

c)

P( z0 Z 0.73 ) = 0.6272

P( Z 0.73 ) - P( Z z0 ) = 0.6272

P( Z z0 ) = 0.1401

P( Z -1.08 ) = 0.1401

z0 = -1.08