(e) Calculate lowest score of the top 10 % of students tail :left ака: са 5:15 M:SS =74.2 • He lowest score of the top xor. of students 6 approximately #274.2. A similar study is undertaken the following year at MGHS and it is found that the scores are still normally distributed, and with the same mean score of 55 but with a standard deviation of 5. (f) Assuming the failing score remains the same for this following year, explain why the percentage of students given a fail score will be less for this new group of students. with a sinaller Standard devidation of s, the distribution of secres you be narrower of more concentrated caustord around the mean compared to the previous yer of is the decrease in s.D means that fle majority of Student's xoles win be sloser to the mean reducing the proportion of stucients woo wone would into the failling range. The exam scores of 780 students from another school, Bondi Secondary School (BSS), were analysed. The scores were found to be normally distributed, and with a mean score of 52 and a standard deviation of 10. These exam scores were compared with those in part (a) from MGHS with a mean score of 55 and a standard deviation of 15. (g) If a student from MGHS obtains an exam score of 82 and a student from BHS obtains an exam score of 75, which student performs better relative to the students from their own school?
(e) Calculate lowest score of the top 10 % of students tail :left ака: са 5:15 M:SS =74.2 • He lowest score of the top xor. of students 6 approximately #274.2. A similar study is undertaken the following year at MGHS and it is found that the scores are still normally distributed, and with the same mean score of 55 but with a standard deviation of 5. (f) Assuming the failing score remains the same for this following year, explain why the percentage of students given a fail score will be less for this new group of students. with a sinaller Standard devidation of s, the distribution of secres you be narrower of more concentrated caustord around the mean compared to the previous yer of is the decrease in s.D means that fle majority of Student's xoles win be sloser to the mean reducing the proportion of stucients woo wone would into the failling range. The exam scores of 780 students from another school, Bondi Secondary School (BSS), were analysed. The scores were found to be normally distributed, and with a mean score of 52 and a standard deviation of 10. These exam scores were compared with those in part (a) from MGHS with a mean score of 55 and a standard deviation of 15. (g) If a student from MGHS obtains an exam score of 82 and a student from BHS obtains an exam score of 75, which student performs better relative to the students from their own school?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
Related questions
Question
Do e, f and g on the GRAPHICS calculator
Transcribed Image Text:Question 4
The exam scores for a group of 780 students at Maquarie Gardens High School (MGHS) are normally
distributed, with a mean score of 55 and a standard deviation of 15.
(a) Complete the scale on the normal distribution graph below.
013%
10
215%
13.54%
25
34-13% 34.13%
40
0.1359 x 780
=109.98
55
Score
70
F106
13.397
2.15%.
(b) Find the number of students who would be expected to obtain a score between 70 and 85
85 100
smo therefore, approximattery 106 students
wond be expected to obtain a
Score between 70 85 in the
group of 78 l students.
(c) The bottom 16% of students will be given a fail. What is the cut-off mark for a fail?
0-13%
0.13 +245 +13.59 = 16%.
ga fus thus, He cut-off
mark for a faul is 40.
(d) What is the probability of a student obtaining a score between 60 and 90?
ac in put
Upper 90
lower: 60
=15
= 55
:: the probability of a student
obtaining
a scole between 60 pad
is approximately 0.361 or $036-1/
Transcribed Image Text:(e) Calculate lowest score of the top 10% of students
tail :left
ака: а.а
5:15
M:SS
=74.2
R
• He lowest score of the top xor. of students
to approximately #274.2.
A similar study is undertaken the following year at MGHS and it is found that the scores are still normally
distributed, and with the same mean score of 55 but with a standard deviation of 5.
(f) Assuming the failing score remains the same for this following year, explain why the percentage of
students given a fail score will be less for this new group of students.
with a sinaller Standard devication of s, the distribution
around the mean compared to the previous yer of Is
the decrease in S.D means that the majority of
Student's xoles with be sloser to
the mean
teclucing the proportion of stucients soovs wone would
into the fallling range.
The exam scores of 780 students from another school, Bondi Secondary School (BSS), were analysed. The
scores were found to be normally distributed, and with a mean score of 52 and a standard deviation of 10.
These exam scores were compared with those in part (a) from MGHS with a mean score of 55 and a
standard deviation of 15.
(g) If a student from MGHS obtains an exam score of 82 and a student from BHS obtains an exam score
of 75, which student performs better relative to the students from their own school?
AUGHS
2 = (82_55)/75 EXS
B$5
2=82-55 = 27
(72-52)/10
2.3
75-82
2732 VE 23 32.3
#
END OF TEST
MGHS
R
BSI
се
on
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