Use the following unit normal tables and accompanying figures to determine the p

Question

Use the following unit normal tables and accompanying figures to determine the probability that a z-score value would fall within each of the specified ranges. To use the tables, click on the Unit Normal. Tables tab beneath the figures, and use the dropdown box to select the desired range of z-score values. A table of the proportions of the normal distribution corresponding to that range of z-scores will appear. If you need a different range of z-scores, simply click on the box again and select a new range. Suggestion: For each of the following five questions, make a sketch of the area under the normal distribution you are seeking. This sketch will help you determine which column(s) of the unit normal tables to use in determining the appropriate probability p(z > 3.6) = P(z > -1.7) = p(z

Explanation / Answer

For calculating the below-mentioned probabilities, we use Normal pobability tables.

1) P[Z>3.6]= 1- P[Z<3.6] (Area to the right of the point 3.6)

By looking up the Normal probability tables for P[Z<3.6]

P[Z>3.6]= 1- P[Z<3.6]= 1- 0.99984= 0.00016

Similarly using the Normal probability tables in the subsequent parts:

2) P[Z>-1.7]= P[Z<1.7]= 0.95543 (Area to the right of the point -1.7)

3) P[Z<1.6]= 0.94520 (Area to the left of the point 1.6)

4) P[0.3<Z<1.3]= P[Z<1.3] - P[Z<0.3]= 0.90320 - 0.61791= 0.28529 (Area between the points 0.3 & 1.3)

5) P[-1.7<Z<0.6]= P[Z<0.6] - P[Z<-1.7]= P[Z<0.6] - P[Z>1.7]= P[Z<0.6] - (1-P[Z<1.7])

=0.72575 - (1 - 0.95543) = 0.68118 (Area between the points -1.7 & 0.6)

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