Question

In: Statistics and Probability

Using the standard normal table, find the value for z0 that makes each statement correct. Enter...

Using the standard normal table, find the value for z0 that makes each statement correct. Enter your answer accurate to the second decimal place, i.e. X.XX where the first x could be 0 like 0.XX

P(Z < z0) = 0.9591 z0 =

P( -z0 < Z < z0 ) = 0.6730 z0 =

P(Z > z0) = 0.9864 z0 =

Solutions

Expert Solution

a) The standardized Z score at the given probability value can be calculated using excel formula or by Z score table. The formula used in excel is =NORM.S.INV(0.9591), this results in the Z score is 1.74.

so, P(Z < Z0) = 0.9591 Z0 = 1.74

b) Since the standardized Z score is calculated from a normal distribution which is symmetrical in nature so, if the probability between Zo is  0.6730, thus the probability at -Zo is (1-0.6730)/2 = 0.1635.

Hence using probability score 0.1635 and excel formula =NORM.S.INV(0.1635) the -Z score is computed as -Zo = -0.98 and using formula =NORM.S.INV(0.1635), Zo is computed as 0.98, thus

P( -Zo < Z < Zo ) =P( -0.98< Z< 0.98) = 0.8365-0.1635 = 0.6730

=> Zo = 0.98

c) Now P(Z > Zo) = 0.9864, since the Z score table and excel formula gives the probability value and Z score from the left of the symmetric distribution. so, P(Z > Zo) = 0.9864 is transformed as P(Z>-Zo) = 1-0.9864 = 0.0136. Now using the probability score in excel formula =NORM.S.INV(0.0136) the Z score is -2.21.

so, P(Z > Zo) = 0.9864. Zo = -2.21

The Z table, in the Z table the probability values are pointed:

orchestra answered 1 year ago
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