From question #8, what proportion is between the mean and 1.95?
The proportion between the mean and 1.95 is 0.95.
To find the proportion of values between the mean and 1.95, we need to calculate the z-scores for both values, and then use the z-table to find the corresponding proportions.
First, let's calculate the z-score for the mean. The z-score formula is:
z = (x - μ) / σ
where:
- x is the value
- μ is the mean
- σ is the standard deviation
Since the mean is the center of the distribution, the z-score for the mean is always zero.
Next, let's calculate the z-score for 1.95. To do this, we need to know the mean and standard deviation of the distribution. If you have that information, please provide it so that I can continue with the step-by-step process.
To determine the proportion of values that fall between the mean and 1.95, we need to calculate the z-scores for both values and then look up the corresponding area under the standard normal distribution curve.
1. Start by finding the z-score for 1.95 using the formula: z = (x - mean) / standard deviation.
- You will need the mean and standard deviation of the data set.
2. Once you have the z-score for 1.95, use a z-score table or a statistical calculator to find the area under the curve between the mean and 1.95. This area represents the proportion of values between the mean and 1.95.
It's important to note that we require the mean and standard deviation of the data set to calculate the z-scores accurately. Without this information, we cannot determine the proportion.