Question

1. What is the difference between a z-score and a z-value? Explain. Explain why the data set below does not resemble a normal distribution: 0, 0, 0, 2, 2, 4, 6, 6, 8, 8, 8 2. Explain what is meant by the following statement "the results are accurate within 3. 2.5%, 27 times in 30"
need solutions for questions 1-3

Answer 1

1) Z-score:A z-score is the number of standard deviations from the mean a data point is.it’s a measure of how many standard deviations below or above the population mean a raw score is.A z-score is also known as a standard score and it can be placed on a normal distribution curve

z = (x – μ) / (σ / √n)

Z-value:The Z-value is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of the standard deviation.You can use the Z-value to determine whether to reject the null hypothesis

2) 0,0,0,2,2,4,6,6,8,8,8

A normal distribution of data is one in which the majority of data points are relatively similar, occurring within a small range of values, while there are fewer outliers on the higher and lower ends of the range of data.

characteristic properties

• They’re all symmetric. The normal distribution cannot model skewed distributions.
• The mean, median, and mode are all equal.
• Half of the population is less than the mean and half is greater than the mean

In the given ata mean = median = 4 but mode is not 4

So its not a normal distribution

3)

27/30 = 0.9 = 90%
90% is the confidence level.

It means that if someone repeats their experiment ,there's a 90% chance that they would be within 2.5% of their original result.