Determine the area under the standard normal curve that lies between ​ (a) Upper Z equals -2.03 and Upper Z equals 2.03​, ​(b) Upper Z equals -1.56 and Upper Z equals 0​, and ​(c) Upper Z equals -1.51 and Upper Z equals 0.68. ​ ​(Round to four decimal places as​ needed.)

Kaycee Roche

Kaycee Roche

Answered question

2021-02-08

Determine the area under the standard normal curve that lies between
(a) Upper Z equals -2.03 and Upper Z equals 2.03​, 
​(b) Upper Z equals -1.56 and Upper Z equals 0​, and 
​(c) Upper Z equals -1.51 and Upper Z equals 0.68.

Answer & Explanation

AGRFTr

AGRFTr

Skilled2021-02-09Added 95 answers

(a) We have:
2.03<z<2.03
Using the appendix's normal probability table, calculate the corresponding probability.
P(Z<2.03) is given in the row starting with -2.0 and in the column starting with .03 of the standard normal probability table in the appendix.
P(Z<2.03) is given in the row starting with 2.0 and in the column starting with .03 of the standard normal probability table in the appendix.
The probability between two boundaries is then the difference between the probabilities to the left of the boundaries.
P(2.03<z<2.03)=P(z<2.03)P(z<2.03)
=0.97880.0212
=0.9576
Hence, the area under the normal distribution between 2.03 and 2.03 is approximately 0.9576.
(b) We have:
1.56<z<0
Using the appendix's normal probability table, calculate the corresponding probability.
P(Z<1.56) is given in the row starting with -1.5 and in the column starting with .06 of the standard normal probability table in the appendix.
P(Z<0) is given in the row starting with 0.0 and in the column starting with .00 of the standard normal probability table in the appendix.
The probability between two boundaries is then the difference between the probabilities to the left of the boundaries.
P(1.56<z<0)=P(z<0)P(z<1.56)
=0.50000.0594
=0.4406
Hence, the area under the normal distribution between -1.56 and 0 is approximately 0.4406.
(c) We have:
1.51<z<0.68
Using the appendix's normal probability table, calculate the corresponding probability.
P(Z<1.51) is given in the row starting with -1.5 and in the column starting with .01 of the standard normal probability table in the appendix.
P(Z<0.68) is given in the row starting with 0.6 and in the column starting with .08 of the standard normal probability table in the appendix.
The probability between two boundaries is then the difference between the probabilities to the left of the boundaries.
P(1.51<z<0.68)=P(z<0.68)P(z<1.51)
=0.75170.0655
=0.6862
Hence, the area under the normal distribution between -1.51 and 0.68 is approximately 0.6862.

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