Final answer:
The percentiles for the standard normal distribution (a) 71st is 0.554, (b) 29th is -0.558, (c) 74th is 0.664, (d) 26th is -0.613, (e) 7th is -1.501.
Step-by-step explanation:
The percentiles for the standard normal distribution can be found using the Z-table or a calculator. The Z-table provides the area under the curve to the left of a given Z-score. To find the percentiles:
For the 71st percentile, we look for the Z-score that has an area to the left of 0.71. Using the Z-table, we find Z = 0.554.
For the 29th percentile, we find the Z-score with an area to the left of 0.29. Using the Z-table, we find Z = -0.558.
For the 74th percentile, we find the Z-score with an area to the left of 0.74. Using the Z-table, we find Z = 0.664.
For the 26th percentile, we find the Z-score with an area to the left of 0.26. Using the Z-table, we find Z = -0.613.
For the 7th percentile, we find the Z-score with an area to the left of 0.07. Using the Z-table, we find Z = -1.501.
Interpolation is used when the area does not exactly match the values in the Z-table.
For example, if we wanted to find the 50th percentile, which is not listed in the Z-table, we would use interpolation to estimate the Z-score.
So therefore the percentiles for the standard normal distribution (a) 71st is 0.554, (b) 29th is -0.558, (c) 74th is 0.664, (d) 26th is -0.613, (e) 7th is -1.501.