Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(z c)=0.0606#, how do you find #c#?

Question

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.  If #P(z > c)=0.0606#, how do you find #c#?

Madeline Adams · Accepted Answer

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HIX Tutor · Answer

undefined Great question! Let’s think this through step by step.

1. **Understand z-scores**: They tell us how far a value is from the mean in standard deviations.

2. **Know what P(z > c) means**: This says the probability of z being greater than c is 0.0606.

3. **Find the probability below c**: We can flip this around. If P(z > c) = 0.0606, then P(z < c) = 1 - 0.0606 = 0.9394.

4. **Use a z-table or calculator**: You need to find the z-score that corresponds to 0.9394.

5. **Look it up**: In a z-table, you find the value where the cumulative area is 0.9394.

6. **Find c**: The z-table or calculator shows that this z-score is approximately 1.55.

7. **So, c = 1.55**.

Does that help? Would you like to go over any part again?

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(z &gt; c)=0.0606#, how do you find #c#?