Question

In: Statistics and Probability

Find the following probabilities based on the standard normal variable Z. (You may find it useful...

Find the following probabilities based on the standard normal variable Z. (You may find it useful to reference the z table. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.)

a. P(−0.98 ≤ Z ≤ −0.62)
b. P(0.06 ≤ Z ≤ 1.62)
c. P(−1.4 ≤ Z ≤ 0.06)
d. P(Z > 3.4)

Solutions

Expert Solution

Solution :

Given that,  

Using standard normal table ,

a.

P(-0.98 z -0.62)

= P(z -0.62) - P(z -0.98 )

= 0.2676 - 0.1635

= 0.1041

P(-0.98 z -0.62) = 0.1041

b.

P(0.06 z 1.62)

= P(z 1.62) - P(z 0.06)

= 0.9474 - 0.5239

= 0.4235

P(0.06 z 1.62) = 0.4235

c.

P(-1.4 z 0.06)

= P(z 0.06) - P(z -1.4)

= 0.5239 - 0.0808

= 0.4431

P(-1.4 z 0.06) = 0.4431

d.

P(z > 3.4) = 1 - P(z < 3.4) = 1 - 0.9997 = 0.0003


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