ind the area of the standard normal distribution that lies to the left of Z = −1.50.
Question
Find the area of the standard normal distribution that lies to the left of Z = −1.50.
Solution
1. Break Down the Problem
To find the area of the standard normal distribution that lies to the left of , we need to look up this value in the standard normal distribution table (Z-table) or use a cumulative distribution function (CDF) for the standard normal distribution.
2. Relevant Concepts
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The cumulative area to the left of a given Z-value can be found using the CDF.
3. Analysis and Detail
- The value we are interested in is .
- By referring to the Z-table or calculating using software, we can find .
4. Verify and Summarize
Upon looking up in the Z-table, we find the corresponding area.
Final Answer
The area of the standard normal distribution that lies to the left of is approximately .
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