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Chapter 6: Problem 15

Obtain the area under the standard normal curve a. to the right of \(z=1.43\) b. to the left of \(z=-1.65\) c. to the right of \(z=-.65\) d. to the left of \(z=.89\)

Short Answer

Expert verified
The areas under the standard normal curve to the right of z=1.43, left of z=-1.65, right of z=-0.65, and left of z=.89 are 0.0764, 0.0495, 0.7422, and 0.8133 respectively.

Step by step solution

01

Determine Z-score values and corresponding areas

First, list the given Z values, for example, \(z=1.43\), \(z=-1.65\), \(z=-0.65\), and \(z=0.89\). Then utilize a standard normal distribution table to find corresponding probabilities or areas under the curve. In a Z-table, the area under the curve to the LEFT of a given Z-score is provided. If the Z-score is positive the Z-table value will be the value to the left, if the Z-score is negative, then subtract the Z-table value from 0.5 to find the left side area.
02

Areas for given Z-scores.

When utilizing the Z-table, a. Right of \(z=1.43\). The Z-table provides the area to the left, which is 0.9236. Consequently, the right side area = \(1 - 0.9236 = 0.0764\). b. Left of \(z=-1.65\). The negative Z-table value gives us 0.0495 to the left for -1.65. c. Right of \(z=-0.65\). Left of -0.65 in the Z-table gives us 0.2578, indicating that right side = \(1 - 0.2578 = 0.7422\). d. Left of \(z=0.89\), we find 0.8133 to the left.
03

Formulate the results

The areas under standard normal curve for given z-scores are, a. Right of \(z=1.43\) is 0.0764, b. Left of \(z=-1.65\) is 0.0495, c. Right of \(z=-0.65\) is 0.7422, and d. Left of \(z=0.89\) is 0.8133.

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