So question. D ON THE GRAPHICS CALCULATOR . Question 4The exam scores for a group of 780 students at Maquarie Gardens High School (MGHS) are normallydistributed, with a mean score of 55 and a standard deviation of 15.(a) Complete the scale on the normal distribution graph below.013%10215%2513.54%0.1359 x 780109.9834-13% 34.13%40that55Score70F18613.3972.15%.85(b) Find the number of students who would be expected to obtain a score between 70 and 85(c) The bottom 16% of students will be given a fail. What is the cut-off mark for a fail?therefore, approximetery 106 Studentswond be expected to obtain aSCOLe between 70 85 in thegroup of the students.0-13%100(d) What is the probability of a student obtaining a score between 60 and 90?GC in putupper 90lower: 6015u=550.13 +215 +13.59bad #us thus, the cut-offmark for a faul is 40.:: the probability of a studentobtaininga score between 60 padis approximately 0.361 or $@36-11-

For the distribution of the exam scores (which is specified to be distributed normally), it is given…

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. 10 215% 25 6 13.54% 0.1359 x 778 0 €185.98 upper 90 lower: 60 = √5 34-13% 34.13% 40 44= 55. 55 Score 70 -106 13.39% (b) Find the number of students who would be expected to obtain a score between 70 and 85 2.15%. 85 O (c) The bottom 16% of students will be given a fail. What is the cut-off mark for a fail? therefore, approximately 106 Students Nond be expected to obtain a SCOLe between 70 85 in the group of 78 e students. (d) What is the probability of a student obtaining a score between 60 and 90? GC in put 0.13 +215+13.59 = 16%. 0-13%. 100 aa #us thus, He cut-off mark for a fan is 40. :: the probability of a student obtaining a scole between 60 pad is approximately 0.361 or $236.11.