Question

In
a certain city within Florida, the IQ scores of its citizens follow
a normal distribution with a mean of 85 and a standard deviation of
10.

a) What percentage of citizens have an IQ score that falls
between 80 and 100?

b) 20% of the city's residents are above what IQ score?

Answer #1

Part a)

X ~ N ( µ = 85 , σ = 10 )

P ( 80 < X < 100 )

Standardizing the value

Z = ( X - µ ) / σ

Z = ( 80 - 85 ) / 10

Z = -0.5

Z = ( 100 - 85 ) / 10

Z = 1.5

P ( -0.5 < Z < 1.5 )

P ( 80 < X < 100 ) = P ( Z < 1.5 ) - P ( Z < -0.5
)

P ( 80 < X < 100 ) = 0.9332 - 0.3085

P ( 80 < X < 100 ) = 0.6247

Part b)

X ~ N ( µ = 85 , σ = 10 )

P ( X > x ) = 1 - P ( X < x ) = 1 - 0.2 = 0.8

To find the value of x

Looking for the probability 0.8 in standard normal table to
calculate Z score = 0.8416

Z = ( X - µ ) / σ

0.8416 = ( X - 85 ) / 10

**X = 93.416
P ( X > 93.416 ) = 0.2**

Suppose the scores on an IQ test approximately follow a normal
distribution with mean 100 and standard deviation 12. Use the
68-95-99.7 Rule to determine approximately what percentage of the
population will score between 100 and 124.

Scores of an IQ test have a bell-shaped distribution with a
mean of 100 and a standard deviation of 20. Use the empirical rule
to determine the following.
(a) What percentage of people has an IQ score between 40 and
160?
(b) What percentage of people has an IQ score less than 80 or
greater than 120?
(c) What percentage of people has an IQ score greater than
160?

Scores of an IQ test have a bell-shaped distribution with a
mean of
100
and a standard deviation of
20.
Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between
80
and
120
(b) What percentage of people has an IQ score less than
40
or greater than
160
(c) What percentage of people has an IQ score greater than
120

Scores of an IQ test have a bell-shaped distribution with a
mean of 100 and a standard deviation of 15. Use the empirical rule
to determine the following.
(a) What percentage of people has an IQ score between 55 and
145?
(b) What percentage of people has an IQ score less than 85 or
greater than 115?
(c) What percentage of people has an IQ score greater
than130?

3. Under any normal distribution of scores, what percentage of
the total area falls…
Between the mean and a score that is one standard deviation
above the mean
Between the mean and two standard deviations below the
mean
Within one standard deviation of the mean
Within two standard deviations of the mean

Scores of an IQ test have a bell-shapped distribution
with a mean of 100 and standard deviation of 15. Use the empirical
rule to determine the following.
A.) What percentage of people has an IQ between 55 and
145?
B.) What percentage of people has an IQ score less than
85 or greater than 115?
C.) What percentage of people has an IQ score greater
than 145?
(Type an integer or decimal.)

Scores of an IQ test have a bell-shaped distribution with a
mean of 100
and a standard deviation of 20.
Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between 40 and
160?
(b) What percentage of people has an IQ score less than 40 or
greater than 160?
(c) What percentage of people has an IQ score greater than
120?

Scores of an IQ test have a bell-shaped distribution with a
mean of 100 and a standard deviation of 20. Use the empirical rule
to determine the following.
(a) What percentage of people has an IQ score between 40 and
160?
(b) What percentage of people has an IQ score less than 60 or
greater than 140?
(c) What percentage of people has an IQ score greater than
140?

Suppose the distribution of IQ scores of adults is normal with a
mean of 100 and a standard deviation of 15. Find IQ score that
separates the top 32 percent of adult IQ scores from the bottom 68
percent. Round your answer to the nearest integer. The IQ score
that separates the top 32 percent of adult IQ scores from the
bottom 68 percent is [IQValue].

1. Scores on a standardized lesson are assumed to follow a
normal distribution, with a mean of 100 and a standard deviation of
32. Five tests are randomly selected. What is the mean test score?
(? ) What is the standard error of the scores? ( ?)
X
XXn
NOTE: The standard error is another name for the standard
deviation of , that is, standard error = .
X
Mean = 100, standard error = 4.53
Mean = 100, standard...

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