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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.

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Solution

1. Break Down the Problem

To find the area of the standard normal distribution that lies to the left of Z=1.50 Z = -1.50 , 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 Z=1.50 Z = -1.50 .
  • By referring to the Z-table or calculating using software, we can find P(Z<1.50) P(Z < -1.50) .

4. Verify and Summarize

Upon looking up Z=1.50 Z = -1.50 in the Z-table, we find the corresponding area.

Final Answer

The area of the standard normal distribution that lies to the left of Z=1.50 Z = -1.50 is approximately 0.0668 0.0668 .

This problem has been solved

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