I know I posted this earlier but I found the answer I just don't know the steps to find it.
Use technology to find the probability associated with the cumulative area to the left of the z
score of the adjusted value of x, 5.5.
P(z < - 0.5546) = 0.2896
If you could just show me the steps to get to the solution I would appreciate it. Thank you
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability to the left of Z. Since Z is negative, it is in the smaller portion.
To find the probability associated with the cumulative area to the left of a specific z-score, you can use a standard normal distribution table or a statistical calculator.
Step 1: Standardize the value of x
In this case, the value of x is 5.5. To use the standard normal distribution table or calculator, you need to convert this value to a standard z-score. A z-score represents the number of standard deviations an observation is from the mean.
To standardize the value, you need to subtract the mean from the value of x, and then divide the result by the standard deviation. Let's assume the mean and standard deviation are μ and σ, respectively.
For example, if the mean (μ) is 0 and the standard deviation (σ) is 1, the standardized z-score can be calculated as follows:
z = (x - μ) / σ
z = (5.5 - 0) / 1
z = 5.5
Step 2: Use the standard normal distribution table or calculator
Now that you have the standardized z-score, you can use a standard normal distribution table or calculator to find the probability associated with the cumulative area to the left of the z-score.
The table will provide probabilities for different z-scores, usually ranging from -3.99 to 3.99. Each value in the table represents the probability of getting a z-score equal to or less than that value.
Look for the closest z-score in the table to the one you calculated in step 1. In this case, the table may not have the exact value of z = 5.5. Instead, you'll find the closest value that has a cumulative probability to the left.
In your example, the closest z-score you can find in the table is z = -0.55. The cumulative probability associated with this z-score is 0.2896.
Therefore, the probability associated with the cumulative area to the left of the z-score of the adjusted value of x (5.5) is 0.2896.