Question

1. What z-score value separates 20% of the distribution in the tail on the left (i.e., the bottom 20% of the distribution) from the rest of the distribution?

2. What z-score value separates 40% of the distribution in the tail on the right (i.e., the top 40% of the distribution) from the rest of the distribution?

*3.* IQ scores are standardized to produce a normal
distribution with a mean of µ = 100 and a standard deviation of σ =
15. Find the proportion of the population in the following IQ
category:

Genius or near genius: IQ greater than 140.

Very superior intelligence: IQ between 120 and 140

Average of normal intelligence: IQ between 90 and 109

Answer #1

(1) z score value that separates the bottom 20%, i.e. 20th percentile of the distribution is -0.842 [From z percentile table]

(2) z score value that separates the top 40% of the distribution, i.e. 60th percentile is 0.253 [From z percentile table]

(3) mean of µ = 100 and a standard deviation of σ = 15

(i) P(X>140) = P(z>(x-µ)/σ)

= P(z>(140-100)/15)

= P(z>2.67)

=1 -P(z<2.67)

= 1-0.9962

= 0.0038 [From z distribution table]

(ii) P(120<x<140) = P((x-µ)/σ<z<(y-µ)/σ)

= P((120-100)/15<z<(140-100)/15)

= P(1.33<z<2.67)

=P(z<2.67)-P(z<1.33)

= 0.9962 - 0.9082

= 0.0880 [From z distribution table]

(iii) P(90<x<109) = P((x-µ)/σ<z<(y-µ)/σ)

= P((90-100)/15<z<(109-100)/15)

= P(-0.67<z<0.6)

=P(z<0.6)-P(z<-0.67)

= 0.7257-0.2514

= 0.4743 [From z distribution table]

S.M.A.R.T. test scores are standardized to produce a normal
distribution with a mean of 230 and a standard deviation of 35.
Find the proportion of the population in each of the following
S.M.A.R.T. categories.
1. Genius: Score of greater than 330.
2. Superior Intelligence: Score between 280 and 330.
3. Average intelligence: Score between 201 and 260.
Please show all work in equations.

1.) If a z-score is larger than _________ it is considered
extreme.
a. +/- 2
b. +/- 0.05
c. +/- 1.64
d. +/- 1.25
2.) For a population with µ = 200 and σ = 25, the distribution
of sample means (based on samples of size n = 25) will have a mean
of _______ and a standard error of _______.
3.) A normal distribution has μ = 70 and σ = 10.
What is the probability of randomly selecting...

6. What proportion of scores in a normal distribution have
z-scores below z = -1.32? (2 points)
7. What proportion of a normal distribution falls between z =
-1.16 and z = 1.16? (2 points)
8. A normal distribution has a mean of µ = 36 with σ = 4. What
proportion of the distribution falls between scores of X = 30 and X
= 38? (3 points)

Question1: It is known the population IQ score follows a normal
distribution with mean as 100, SD as 10. A researcher is interested
in studying if the average IQ of students from statistics courses
on average has a higher IQ score than the population IQ score. To
test this hypothesis, the researcher randomly collected a sample of
25 students from statistic class, the mean IQ score for this sample
is 110. Compete for the hypothesis test at significant level.
Step...

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. What is the z-score corresponding to P66
2. What is the z-score corresponding to Q1
3. For a normal distribution with μ μ = 40 and σ σ = 3.1,
determine P(x > 43.906).
4. For a standard normal distribution, determine the z-score,
z0, such that P(z > z0) = 0.0931.
5. For a standard normal distribution, determine the z-score,
z0, such that P(z < z0) = 0.9698.
6. From a normal distribution with μμ = 76 and σσ...

The population IQ score was collected from a national-wide test.
The mean population IQ score is 101 and with a stand deviation of
15. The data of original population follows the normal
distribution.
Use the Z-score table provided to answer the following
questions:
(1) What is the Z score for IQ score = 95?
Answer: (Please report your answer to 3 decimal
places.)
(2) What is the Z score for IQ score = 110?
Answer: (Please report your answer to 3 decimal...

In the example in the previous item, using a z-table what is the
minimum z-score a student can have on the EI test and be in the
top
a) 60%
b) 55%
c) 85%
d) 40%
e) 15%
previous question-
Suppose that student scores on an emotional intelligence (EI)
test are normally distributed. Using a z-table (normal curve
table), what percentage of students have z-scores
a) above .10
b) below .10
c) above .20
d) below .20
e) above 1.33...

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

Test D: population mean = 150 and standard deviation = 20.
Danyang’s test score is X = 140.
D1.1. Draw the normal curve for this distribution.
D1.2. State the value of a score X in the distribution that
corresponds to the 99.87th percentile rank.
D1.3. Compute the person’s z-score.
D1.4. Write an X in the distribution’s horizontal axis where the
person’s score is located.
D1.5. State the area (proportion) of the curve between the mean
and the...

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