Use the following Normal Distribution table to calculate the area under the Normal Curve (Shaded area in the Figure) when Z=1.3 and H=0.05; Assume tha

Efan Halliday

Efan Halliday

Answered question

2021-06-05

Use the following Normal Distribution table to calculate the area under the Normal Curve (Shaded area in the Figure) when Z=1.3 and H=0.05;
Assume that you do not have vales of the area beyond z=1.2 in the table; i.e. you may need to use the extrapolation.
Check your calculated value and compare with the values in the table [for z=1.3 and H=0.05].
Calculate your percentage of error in the estimation.
How do I solve this problem using extrapolation?
Z+HProb.Extrapolation1.200000.38490Differences1.210000.386900.002001.220000.388800.001901.230000.390700.001901.240000.392500.001801.250000.394400.001901.260000.396200.001801.270000.398000.001801.280000.399700.001701.290000.401500.001801.300000.403200.001701.310000.404900.001701.320000.406600.001701.330000.408300.001701.340000.410100.001801.350000.411900.00180

Answer & Explanation

curwyrm

curwyrm

Skilled2021-06-06Added 87 answers

Step 1
Here, we have to use the technique of extrapolation for finding the probability for the z=1.35(Z=1.3 & H=0.05). Let us see this discuss this question step by step given as below:
For using extrapolation we need the values for the row of z=1.2
The values for the row z and columns H are given as below:
By using the extrapolation, we get
Z+HProb.Extrapolation1.200000.38490Differences1.210000.386900.002001.220000.388800.001901.230000.390700.001901.240000.392500.001801.250000.394400.001901.260000.396200.001801.270000.398000.001801.280000.399700.001701.290000.401500.001801.300000.403200.001701.310000.404900.001701.320000.406600.001701.330000.408300.001701.340000.410100.001801.350000.411900.00180
We get P(Z<1.35)=0.4119 by using the extrapolation however the probability by using the table is given as 0.4115.
This means there is a very small difference observed due extrapolation.

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