Question

Defined the Z score and its importance in normal distribution ?

Answer #1

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

A normal distribution has μ = 34 and σ = 5. (a) Find the z score
corresponding to x = 29. (b) Find the z score corresponding to x =
46. (c) Find the raw score corresponding to z = −3. (d) Find the
raw score corresponding to z = 1.5.

A normal distribution has μ = 30 and σ =
5.
(a) Find the z score corresponding to
x = 25.
(b) Find the z score corresponding to
x = 41.
(c) Find the raw score corresponding to
z = −3.
(d) Find the raw score corresponding to
z = 1.5.

A normal distribution has μ = 24 and σ =
5.
(a) Find the z score corresponding to
x = 19.
(b) Find the z score corresponding to
x = 37.
(c) Find the raw score corresponding to
z = −2.
(d) Find the raw score corresponding to
z = 1.7.

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.

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

Find the z-score such that:
The area under the standard normal model to its left is 0.9412 z
=
The area under the standard normal model to its right is 0.1576
z =

Assume a normal distribution. (Give your answer correct to two
decimal places.)
(a) Find the z-score associated with the 59th percentile.
(b) Find the z-score associated with the 82nd percentile.
(c) Find the z-score associated with the 92nd percentile.

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?

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

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