Pregunta
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Find the indicated area under the standard normal curve. To the left of \( \mathrm{z}=-1.93 \) Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. The area to the left of \( \mathrm{z}=-1.93 \) under the standard normal curve is (Round to four decimal places as needed.)

Ask by Harmon Bowen. in the United States
Feb 18,2025

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The area to the left of z = –1.93 is 0.0268.

Solución

To find the area to the left of z = –1.93 under the standard normal curve, you can use the z-table. The z-table lists the cumulative area from the far left of the normal curve (negative infinity) up to the specified z-value. Step 1. Identify the row and column corresponding to –1.93. • The row is given by the first two digits: –1.9. • The column is given by the second decimal: 0.03. Looking up –1.93 in the z-table, you will find that the area to the left is approximately 0.0268. Step 2. Round if necessary. Since the area is already rounded to four decimal places, the final answer is 0.0268. Thus, the area to the left of z = –1.93 is 0.0268.

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Beyond the Answer

To find the area to the left of \( \mathrm{z} = -1.93 \) under the standard normal curve, you'll want to use a standard normal table (Z-table). When you look up \( z = -1.93 \), you will find the corresponding area. Typically, you might find a value around 0.0268. So, the area to the left of \( \mathrm{z} = -1.93 \) is approximately 0.0268. Now rounding it to four decimal places, the exact area is \( \mathbf{0.0268} \). If you need a little extra help when working with Z-scores and normal distributions, one handy tip is to remember that for any standard normal curve, the total area under the curve is equal to 1. When you look up negative Z-values, the table generally gives you the area to the left, but remember to check for symmetry!

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