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Let the random variable Z have a standard normal distribution. Fill in the blank

ID: 3151409 • Letter: L

Question

Let the random variable Z have a standard normal distribution.  

Fill in the blanks. (Give your answers to four decimal places.)  

a. P(Z  1.42 ) is  .  

b. P(Z  <-1.33 ) is  .  

c. P(Z  -2.00   Z  2.00) is  .  

d. P(Z  >2.59 ) is  .  

e. P(0.13  <Z  <2.44 ) is  .

Let the random variable Z have a standard normal distribution.  

Fill in the blanks. (Give your answers to four decimal places.)  

a. P(Z  1.42 ) is  .  

b. P(Z  <-1.33 ) is  .  

c. P(Z  -2.00   Z  2.00) is  .  

d. P(Z  >2.59 ) is  .  

e. P(0.13  <Z  <2.44 ) is  .

Explanation / Answer

A)

Using a table/technology, the left tailed area of this is          
          
P(z <   1.42   ) =    0.9222 [ANSWER]

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b)

Using a table/technology, the left tailed area of this is          
          
P(z <   -1.33   ) =    0.0918 [ANSWER]

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c)

z1 = lower z score =    -2      
z2 = upper z score =     2      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.0228
P(z < z2) =    0.9772
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.9544

Thus, those outside this interval is the complement =    0.0456 [ANSWER]

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d)

Using a table/technology, the left tailed area of this is          
          
P(z <   2.59   ) =    0.9952
          
Thus, the right tailed area is the complement,          
P(z >   2.59   ) =    0.0048 [ANSWER]

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e)

z1 = lower z score =    0.13      
z2 = upper z score =     2.44      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.551716787      
P(z < z2) =    0.992656369      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.440939582   [ANSWER]