Jimmy is the education consultant of a tutorial school, which arranges preparatory classes for IELT examination. He randomly checks the mock examination result of 22 students in the school and the results are as follow: 7.9 8.2 7.8 5.4 6.8 6.8 7.1 7.2 7.9 8.1 7.6 7.8 5.8 6.3 7.7 7.7 8.3 8.3 4.7 5.1 7.3 6.5 (a) Write a report to reflect students’ ability in the mock examination. The report needs to include the average performance, the median, the standard deviation, the bottom 20% and top 10% performance level. (b) The manager asks if the distribution of the examination result looks like a normal distribution. Answer his question by reviewing the skewness of the data with detailed calculation. (c) There are 18 students in Alex’s class. By using the sampled data as a reference to project the chance an individual student can get more than 6 marks and assume students’ result are independent, calculate the probability that more than 80% of Alex’s students can score higher than 6 marksin the mock examination.
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.
Question 2
Jimmy is the education consultant of a tutorial school, which arranges preparatory classes for IELT
examination. He randomly checks the mock examination result of 22 students in the school and the results
are as follow:
7.9 8.2 7.8 5.4 6.8 6.8 7.1 7.2 7.9 8.1 7.6
7.8 5.8 6.3 7.7 7.7 8.3 8.3 4.7 5.1 7.3 6.5
(a) Write a report to reflect students’ ability in the mock examination. The report needs to include the
average performance, the
(b) The manager asks if the distribution of the examination result looks like a
his question by reviewing the skewness of the data with detailed calculation.
(c) There are 18 students in Alex’s class. By using the sampled data as a reference to project the chance an
individual student can get more than 6 marks and assume students’ result are independent, calculate the
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