. In terms of the mean and standard deviation:

- What does it mean to say that a particular value of x has a standard score of +1.5?
- What does it mean to say that a particular value of x has a z-score of -2.6?
Please show all work.

If a value of x has a standard score of 1.5, this means that x is 1.5 standard deviations above the mean.

The mean divides a distribution in half. Half the values are above the mean and half are below the mean.

I'll let you try the second question on your own.

I hope this helps.

I really don't understand statistics and am not sure if I am trying to make it harder than it needs to be, but I am lost!

Please only post your questions once. Repeating posts will not get a quicker response. In addition, it wastes our time looking over reposts that have already been answered in another post. Thank you.

See your other post.

To understand what it means to say a particular value of 𝑥 has a standard score of +1.5 and a z-score of -2.6, we need to understand the concepts of standard score and z-score.

Standard score, also known as z-score, indicates how many standard deviations a data point is from the mean of a distribution. It is a standardized measurement that allows us to compare and interpret values in different distributions by converting them into a common scale.

To calculate the standard score (z-score) of a value 𝑥, we use the formula:
𝑧 = (𝑥 - 𝜇) / 𝜎

Where:
- 𝑧 is the standard score (z-score)
- 𝑥 is the data value
- 𝜇 is the mean of the distribution
- 𝜎 is the standard deviation of the distribution

Now let's calculate and interpret the given values:

1. Standard score of +1.5
To calculate the mean and standard deviation, we need more information about the distribution. Let's assume we are working with a normal distribution.
- For a standard score of +1.5, we know that 𝑧 = 1.5.
- We rearrange the formula 𝑧 = (𝑥 - 𝜇) / 𝜎 to solve for 𝑥:
𝑥 = 𝜇 + 𝑧𝜎
- Since 𝑧 = 1.5, we can substitute it into the equation along with the mean (𝜇) and standard deviation (𝜎) values of the distribution to find the corresponding 𝑥 value.

2. Z-score of -2.6
Similarly, let's assume we are working with a normal distribution.
- For a z-score of -2.6, we know that 𝑧 = -2.6.
- Using the rearranged formula 𝑥 = 𝜇 + 𝑧𝜎, we can substitute 𝑧 = -2.6, 𝜇, and 𝜎 into the equation to find the corresponding 𝑥 value.

Since we need additional information about the distribution (specifically the mean and standard deviation) to calculate the corresponding 𝑥 values, I am unable to provide the exact calculations without more details.