P ( z < -1.76) = .0392 P ( z < 4.18) > P ( z < 3.89) = 1.0000 1.5 .99990 The pro

Question

P(z < -1.76) = .0392

P(z < 4.18) > P(z < 3.89) = 1.0000

1.5     .99990

The probability P(z < -1.76) is found at the intersection of the -1.7 row and the .06 column of the z table (table of standard normal probabilities). The result is

P(z < -1.76) = .0392

as shown in the following figure:

In other words, in a long sequence of observations, roughly 3.9% of the observed z values will be smaller than -1.76. Similarly,

P(z .058) = entry in 0.5 row and .08 column of table of standard normal probabilities = .7190

as shown in the following figure:

Now consider P(z < -4.12). This probability does not appear in table of standard normal probabilities; there is no -4.1 row. However, it must be less than P(z < -3.89), the smallest z value in the table, because -4.12 is farther out in the lower tail of the z curve. Since P(z < -3.89) = .0000 (that is, zero to four decimal places), it follows that

P(z < -4.12) 0

Similarly,

P(z < 4.18) > P(z < 3.89) = 1.0000

from which we conclude that

P(z < 4.18) 1

What is the total area under the z curve?

1.5     .99990

Find the probability P(z > -1.76)..96081     .9806.0392

Explanation / Answer

the probability that P[z>-1.76] is

P[z>-1.76]=1-P[z<-1.76]

now given in the question that P[z<-1.76]=0.392

hence P[z>-1.76]=1-0.0392=0.96081   [answer] [the first choice]

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