14. A group of 78 third-grade students in a Midwestern elementary school took a "self-concept" test that measured how well they felt about themselves. Higher scores indicate more positive self-concepts. A histogram and some summary statistics from Minitab for these students' self-concept scores are given below 15 10 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Sef-concept Descriptive Statistics: SelfConc StDev 12,35 Median Q3 65.00 Maximum Q1 50.00 Minimum Variable N SelfConc 78 Mean 56.85 20.00 59.00 84.00 (a) One student in the group had a self-concept score of 62. Calculate and interpret this student's z-score. Kuanbay
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![e /home/chronos/u-33cab27
14. A group of 78 third-grade students in a Midwestern elementary school took a "self-concept"
test that measured how well they felt about themselves. Higher scores indicate more
positive self-concepts. A histogram and some summary statistics from Minitab for these
students' self-concept scores are given below
15
10
5
70
75 80 85
45 50
Sef-concept
20
25
30
35
40
55
60
65
Descriptive Statistics: SelfConc
Mean
56.85
Q3
65.00
Maximum
84.00
Median
Q1
50.00
StDev
Minimum
Variable N
SelfConc 78
12.35
20.00
59.00
(a) One student in the group had a self-concept score of 62. Calculate and interpret this
student's z-Score.
© 2017 BFW Publishers StarnesTabor Statistics and Probability with Applications 3/e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd91cdba-d936-4251-9a9d-c5e338e06f7c%2Fb87e6e17-a4bb-4540-826d-48bed9a14443%2Fck7jj_processed.jpeg&w=3840&q=75)
![(b) Interpret the standard deviation.
(c)
What percentage of the third graders scored less than 30 on the self-concept test?
(d) Use the rule to check if 84 is an outlier.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd91cdba-d936-4251-9a9d-c5e338e06f7c%2Fb87e6e17-a4bb-4540-826d-48bed9a14443%2Fhllldh_processed.jpeg&w=3840&q=75)
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