Determine the following standard normal (z) curve areas. (Round your answers to four decimal places.)
a) the area under the z curve to the left of 1.74
b) the area under the z curve between −2 and 2
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a) The area under the z curve to the left of 1.74 can be found using a standard normal table or a calculator. Using a standard normal table, we can look up the value for 1.74 in the z column and find the corresponding area to the left. The closest value in the table is 1.7, which has an area of 0.9554. The area under the z curve to the left of 1.74 is approximately 0.9554.
b) The area under the z curve between -2 and 2 can be found by calculating the area to the left of 2 and subtracting the area to the left of -2. Using a standard normal table, we can look up the value for 2 in the z column and find the corresponding area to the left. The closest value in the table is 1.9, which has an area of 0.9713. Similarly, we can look up the value for -2 in the z column and find the corresponding area to the left. The closest value in the table is -2.0, which has an area of 0.0228. Therefore, the area under the z curve between -2 and 2 is approximately 0.9713 - 0.0228 = 0.9485.
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