I have no idea on how to answer this question...
"Use technology or a standard normal distribution table to find the area to the left of z=1.58.
Do I plug in 1.58 in my calculator to find the answer?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. It will be the larger portion.
To find the area to the left of z=1.58 using either technology or a standard normal distribution table, you can follow these steps:
1. If you have a scientific calculator, you can directly plug in the value of z=1.58 and use the calculator's normal distribution function. Look for a function like "normcdf" or "normalCDF" in the calculator. Input the mean (µ) and standard deviation (σ) of the normal distribution you are working with, and specify the lower bound as negative infinity (or a very large negative number) and the upper bound as 1.58. The result will give you the area to the left of z=1.58.
2. If you don't have access to a calculator with a normal distribution function, you can use a standard normal distribution table. This table provides probabilities for values of the standard normal distribution from z=0 to z=3.99. Since you are looking for the area to the left of z=1.58, you will need to look up the value for 1.58 in the table.
Locate the row corresponding to 1.5 in the table and the column corresponding to 0.08 (or 0.08 rounded to two decimal places). The value where the row and column intersect will give you the area to the left of z=1.58. Make sure to refer to the table's instructions for interpreting the values correctly. Keep in mind that some tables may provide the area to the right of the given value, so you may need to subtract the value from 1 to get the area to the left.
Remember that the area to the left of any specific z-value represents the cumulative probability from the left tail to that z-value.
To find the area to the left of z = 1.58 using a standard normal distribution table or technology, you would need to follow these steps:
1. Standardize the value you want to find the area for. In this case, you want to standardize z = 1.58.
2. The standardization formula is: z = (x - μ) / σ, where x is the value you want to standardize, μ is the mean, and σ is the standard deviation. However, since we are working with a standard normal distribution table, the mean is always 0 and the standard deviation is always 1.
3. So, to standardize z = 1.58, you would use the formula: z = (1.58 - 0) / 1 = 1.58.
4. Now, you have standardized your z-value, and you can use a standard normal distribution table or technology to find the area to the left of z = 1.58.
If you are using a standard normal distribution table:
5. Look up the standardized z-value of 1.58 in the table, and locate the corresponding area in the table.
If you are using technology like a calculator or statistical software:
5. Use the cumulative distribution function (CDF) or the normal distribution function with the appropriate parameters to find the area to the left of z = 1.58.
Plugging in 1.58 directly into a calculator will not provide the area to the left of z = 1.58, as the calculator does not inherently know the context of the z-value. You need to standardize the value and use a standard normal distribution table or technology to find the area.