In: Statistics and Probability
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.)
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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