A) how much of the data lies below the value corresponding to Z=1.2? B) how much

Question

A) how much of the data lies below the value corresponding to Z=1.2?
B) how much of the data lies between the values corresponding to Z=1.2 and Z=1.4?
C) how much of the data lies between the values corresponding to Z=-1.2 and Z=1.4?
(1) For the following questions, consider a data set that exhibits a normal distribution. Report the answers to the nearest 0.01%. (a) How much of the data lies below the value corresponding to Z 1.2? (b) How much of the data lies between the values corresponding to Z 1.2 and Z m 1.4? (c) How much of the data lies between the values corresponding to Z 1.2 and Z 1.4?

Explanation / Answer

SolutionA:

We conclude that:

P ( Z<1.2 )=0.8849

   =0.8849=88.49%

88.49%

Solutionb:

Step 2: To find the probability of P (1.2<Z<1.4), we use the following formula:

P (1.2<Z<1.4 )=P ( Z<1.4 )P (Z<1.2 )

Step 3: P ( Z<1.4 ) can be found by using the following standard normal table.

From Standard Normal Table

We see that P ( Z<1.4 )=0.9192.

Step 4: P ( Z<1.2 ) can be found by using the following standard normal table.

From Standard Normal Table

We see that  P ( Z<1.2 )=0.8849.

At the end we have:

P (1.2<Z<1.4 )=0.0343=3.43%

Answer 3.43%

Solutionc:

Step 2: To find the probability of P (1.2<Z<1.4), we use the following formula:

P (1.2<Z<1.4 )=P ( Z<1.4 )P (Z<1.2 )

Step 3: P ( Z<1.4 ) can be found by using the following standard normal table.

From Standard Normal Table

We see that P ( Z<1.4 )=0.9192.

Step 4: P ( Z<1.2 ) can be found by using the following fomula.

P ( Z<a)=1P ( Z<a )

After substituting a=1.2 we have:

P ( Z<1.2)=1P ( Z<1.2 )

P ( Z<1.2 ) can be found by using the following standard normal table.

From Standard Normal Table

We see that P ( Z<1.2 )=0.8849 so,

P ( Z<1.2)=1P ( Z<1.2 )=10.8849=0.1151

At the end we have:

P (1.2<Z<1.4 )=0.8041

=0.8041*100=80.41%

Answer 80.41%

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5 0.504 0.508 0.512 0.516 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.591 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.695 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.719 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.758 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.791 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.834 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 1.2 0.8849

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