Question

Calculate the area under the standard normal curve to the left of these values. (Round your answers to four decimal places.)

(a) z = 1.6
(b)z = 1.89
(c)z = 0.60
(d)z = 4.18

Answer 1

To find the area under the standard normal curve to the left of given z-scores, use a Z-table to locate the corresponding cumulative probabilities. Round each area to four decimal places and use interpolation if necessary.

Step-by-step explanation:

To calculate the area under the standard normal curve to the left of specific z-scores, you will use a Z-table.

1. For z = 1.6, locate the corresponding area in the Z-table.
2. Repeat this process for z = 1.89, z = 0.60, and z = 4.18, finding the left-hand area for each.
3. If the exact z-score is not listed, find the closest value or interpolate between the two surrounding values.
4. Most Z-tables give the area to the left as a cumulative probability.
5. The desired areas will each round to four decimal places, following the standard convention for reporting statistical results.

For instance, if we know the areas for z = -0.40 and z = 1.5, we can calculate the area between them. In contrast, to find the critical value such as the one that leaves an area to the right of 0.01, you would search the Z-table for the value corresponding to the 0.99 cumulative area. Remember that the area under the curve to the left of a z-score is equivalent to the cumulative probability of observing a value less than or equal to that z-score in a normally distributed population.