Find the area to the right of the z-score 1.40 and to the left of the z-score 1.

Question

Find the area to the right of the z-score 1.40 and to the left of the z-score 1.58 under the standard normal curve. Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0951 09599 09608 0.9616 0.9625 0,9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9700 1.9 0.9713 0.9719 0.0726 0.9782 0978 0.0744 0,0750 0.9756 00761 0,9767 3 Use the value(s) from the table above

Explanation / Answer

In this table the values we are given are of P(Z< z).

So if you have to find the area to the left of z-score 1.58 i.e., P(Z<1.58),then

Step1:  look out for 1.5 in the first seperated column and note the row in front of 1.5.

Step2: Corresponding to the row you have selected in step1, lookout for 0.08 in first seperated row and note the column of 0.08.

Step3. Note the value at the intersection of row you selected in step 1 and column at step 2. In this case it is 0.9429.

Hence,  the area to the left of z-score 1.58 i.e., P(Z<1.58) is 0.9424.

Now, the area to the right of z-score 1.40 i.e., P(Z>1.40) can be calculated by

Step1 Repeat all the steps mentioned above and find the value of P(Z<1.40). Which is 0.9192.

Step2 P(Z>1.40)= 1- P(Z<1.40)= 1 - 0.9192 = 0.0808.

Hence, the area to the right of z-score 1.40 i.e., P(Z>1.40) is 0.0808.

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