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Understanding Z-Scores and Their Interpretations

Total questions: 20

Worksheet time: 26mins

Name
Class
Date
1.

What is the formula for finding the z-score?

a)
z = (X - σ) / μ
b)
z = (X + μ) / σ
c)
z = (X - μ) / σ
d)
z = (μ - X) / σ
2.

Which of the following is the correct interpretation of a z-score?

a)

The average of all data points in a dataset

b)

The sum of all data points divided by the number of data points

c)

The difference between the highest and lowest data points

d)

The number of standard deviations a data point is from the mean

3.

If a data point has a z-score of 2, what does this imply?

a)

The data point is two standard deviations below the mean

b)

The data point is two standard deviations above the mean

c)

The data point is at the mean

d)

The data point is an outlier

4.

What are the percentiles to know on a CRF graph?

a)
25th, 50th, and 75th percentiles
b)
5th, 15th, and 95th percentiles
c)
10th, 30th, and 90th percentiles
d)
20th, 40th, and 60th percentiles
5.

What is a Z-score?

4 lines
6.

If a distribution is right skewed, what does that mean?

a)
It means that the distribution has a longer tail on the left side.
b)

It indicates that the median is less than the mean.

c)
It means that the distribution has a longer tail on the right side.
d)
It suggests that most values are concentrated on the right side.
e)

I don't know.

7.

If a distribution is left skewed, what does it mean?

a)
It means that the distribution has a longer tail on the right side.
b)

The mean is less than the median.

c)
It means that the distribution has a longer tail on the left side.
d)
It suggests that the data is uniformly distributed.
e)

I don't know.

8.

If a distribution is symmetric, what does that mean?

a)
A symmetric distribution is always uniform in shape.
b)
A symmetric distribution has equal values on both sides of its center.
c)
A symmetric distribution has unequal values on both sides.
d)
A symmetric distribution has a single peak on one side.
e)

Mean=Median

9.

Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and variability of a distribution.

4 lines
10.

What's the total area of a density curve?

a)
1.5
b)
2
c)
0.5
d)
1
11.

What does a z-score of 0 indicate about a data point?

a)

The data point is one standard deviation below the mean

b)

The data point is at the mean

c)

The data point is an outlier

d)

The data point is one standard deviation above the mean

12.

Which of the following best describes a normal distribution?

a)

A distribution with a single peak and symmetrical tails.

b)

A distribution with multiple peaks.

c)

A distribution with a longer tail on one side.

d)

A distribution with no peaks.

13.

What is the mean of a standard normal distribution?

a)

1

b)

2

c)

0

d)

-1

14.

Which of the following measures is not affected by extreme values?

a)

Mean

b)

Median

c)

Range

d)

Standard Deviation

15.

The height of a specific species of trees follows a Normal distribution with a mean of 35 feet and a standard deviation of 6 feet.
a) What percent of trees are taller than 40 feet?

4 lines
16.

The daily calorie intake of a gymnast is Normally distributed with a mean of 3,200 calories and a standard deviation of 400 calories.
a) What percent of gymnasts consume more than 3,600 calories in a day?

4 lines
17.

The number of eggs produced by hens on a farm follows a Normal distribution with a mean of 300 eggs per year and a standard deviation of 50 eggs. The farm sells eggs for $0.25 each. If a hen’s production is at the 90th percentile of the distribution, how much revenue would the farm make from that hen’s eggs?

4 lines
18.

A coffee shop tracks the number of cups of coffee sold per day, which follows a Normal distribution with a mean of 200 cups and a standard deviation of 30 cups. The shop makes $4.00 per cup of coffee sold. If the number of cups sold on a given day is at the 15th percentile of the distribution, how much revenue does the coffee shop make that day?

4 lines
19.

The distribution of weights for a specific type of fish caught in a lake is strongly skewed to the left, with a mean of 12 pounds and a standard deviation of 3 pounds. The distribution of z-scores for those weights is:

a)

Normally distributed with mean 0 and SD 1.

b)

Normally distributed with mean 12 and SD 3.

c)

Skewed to the left with mean 12 and SD 3.

d)

Skewed to the left with mean 0 and SD 1.

20.

Which measure of central tendency is most affected by outliers?

a)

Range

b)

Mean

c)

Median

d)

Mode