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. 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 marks in 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.
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
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(a) Write a report to reflect students’ ability in the mock examination.
average performance, themedian , 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 marks in the mock examination.
I need (a) (b) (c) answer
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