For the standard normal distribution, find the value of c such that:
P(z > c) = 0.3382
To find the value of \( c \) for which \( P(Z > c) = 0.3382 \) in a standard normal distribution, we need to refer to the standard normal distribution table or use statistical software that can provide the needed value. Since we are looking at the area to the right of \( c \), we are interested in the upper tail of the distribution.
The standard normal distribution table typically gives cumulative probabilities from the left up to a certain z-value. Therefore, we need to find the value of \( c \) for which the cumulative distribution function (CDF) to the left of \( c \) equals \( 1 - 0.3382 = 0.6618 \).
I will now look up the z-value that corresponds to the cumulative probability of \( 0.6618 \) or, equivalently, use a statistical tool to find it.
Using statistical software or a calculator with inverse cumulative distribution function capabilities (often represented as the invNorm function), we input the desired cumulative probability of \( 0.6618 \) to find the corresponding z-score.
For example, in many software packages or calculators, you could use the following command or equivalent:
```
invNorm(0.6618)
```
If you do not have access to software or a calculator that can perform this function, you can use the z-table manually. Find the closest value to \( 0.6618 \) in the table and note the corresponding z-value.
For this example, let's assume that the correct value of \( c \) is found to be approximately 0.42 using statistical software or a z-table. This means that if the standard normal variable Z follows \( N(0,1) \), then the value of \( c \) for which \( P(Z > c) = 0.3382 \) is approximately 0.42.
Please note that this value is an approximation, as the exact value would depend on the precision of the z-table or software used.