Question

What are the characteristics of a standard normal distribution? Describe some applications for applying a z-score to normalize data. What are the advantages? Disadvantages?

Answer #1

**Characteristics of standard normal
distribution:**

1) Continuous Random Variable.

2) Mound or Bell-shaped curve.

3) The normal curve extends indefinitely in both directions,
approaching, but never touching, the horizontal axis as it does
so.

4) Unimodal

5) Mean = Median = Mode

6) Symmetrical with respect to the mean

That is, 50% of the area (data) under the curve lies to the left
of

the mean and 50% of the area (data) under the curve lies

to the right of the mean.

7) (a) 68% of the area (data) under the curve is within one

standard deviation of the mean

(b) 95% of the area (data) under the curve is within two

standard deviations of the mean

(c) 99.7% of the area (data) under the curve is within three

standard deviations of the mean

8) The total area under the normal curve is equal to 1.

**Applications for applying a- score to normalize
data:**

With a normal distribution of a variable, the mean is the center of the distribution, while the standard deviation shows the level of variability that exists. When you know the value of a variable that is normally distributed, you can calculate the z-score by using the formula:

Z-score:

When you are interested in determining the probability of a specific value occurring, you can use a z-table to look up areas for a calculated z-score to determine the area under the curve of any normal distribution. This can tell you the chance of a value occurring. It should be noted that not all z-score tables are the same.

z-Table

Table for looking up the area starting at z = 0 for a positive z-score

value - mean standard deviation

**Advantages to normalization**

1) Avoids data modification (INSERT/DELETE/UPDATE) anomalies as
each data item lives in One place

2) Greater flexibility in getting the expected data in atomic
granular

3) Normalization is conceptually cleaner and easier to maintain and
change as your needs change

4) Fewer null values and less opportunity for inconsistency

5) A better handle on database security

6) Increased storage efficiency

**Disadvantages of normalization**

1) Requires much more CPU, memory, and I/O to process thus
normalized data gives reduced database performance

2) Requires more joins to get the desired result. A poorly-written
query can bring the database down

3) Maintenance overhead. The higher the level of normalization, the
greater the number of tables in the database

Need some assistance:
1. In a standard normal distribution, what is the percentile
score of a data point with a Z-score of 1?
50.00
84.13
93.33
97.73
2. Mean hourly wage in the construction industry is $19.45 and
standard deviation is $3.94. What is the probability that a worker
receives less than minimum wage, which is $14/hour?
4.75%
8.33%
91.67%
95.25%
3. The average price of milk available in supermarkets in 2015
is $4.98/gallon. The standard deviation is $0.72. What...

Find the indicated z score. The graph depicts the standard
normal distribution with mean 0 and standard deviation 1. z0.2266
0

Using a normal distribution and z score formula answer
the following questions
a. Find the score that cuts off the bottom 35% of the
normal curve
b. Find the data value to the nearest whole number that
cuts off the op 10% of the curve given
that the mean is 75 and sample standard deviation is
5
C Find the z scores that cut off the middle 60% of the
normal curve.

Find the indicated z score. The graph depicts the standard
normal distribution with mean 0 and standard deviation 1. Shaded
area is 0.4013.

1. True or False.
1a. z-scores follow a standard normal distribution.
1b. A z-score indicates how many standard deviations a value is
1b. above or below the mean.
1c. Point estimators are always good estimates of population
parameters, and there are never any deviations or errors
1d. The process of converting a value x from a normal
distribution to a z-score is known as standardization

Basic computation: z score and raw score. a normal distribution
has mean = 10 and a standard deviation = 2. a) find the z score
corresponding to x=12. b) find the z score corresponding to x=4. c)
find the raw score corresponding to z= -2. d) find the raw score
corresponding to z= -1.2

1. What proportion of scores in a normal distribution lie
between the mean and a z-score of -0.44?
2. What proportion of scores in a normal distribution are
greater than or equal to a z-score of -2.31?

1) What is a z-score?
2) What does normal population distribution mean?
3) What information are obtained from a standard normal
table?

Use the standard normal (z score) table to find: P(-1.00 ≤
z)
Find the probability that a data value picked at random from a
normal population will have a standard score (z) that lies between
the following pairs of z-values. z = 0 to z = 2.10

Defined the Z score and its importance in normal distribution
?

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