Refer to the Standard Normal cumulative probability table below or download the table from here.
Source of table: http://www.z-table.com/
Below is a list of questions based on the Statistics module 1.
Normal Distribution and Z-scores
Refer to the sample table of data sheet of marks of ten students in a test. Assume the marks of the students are normally distributed. Refer to normal probability table for Z scores, they are freely available on internet. Refer to the Module 1 Statistics module before attempting this exercise.
1. Calculate the mean (average) and standard deviation of the sample using excel. Also, calculate the standard deviation using mean method using excel. (69.6,8.66)
2. Person 4 scored 73. What’s the corresponding percentile. The percentile its better than.
(4.27%; 65.29%) Use Norm.dist function in excel. NORM.DIST(73,69.6,8.65, False) for the first one and NORM.DIST(73,69.6,8.65, True for second). The solution has been corrected and the second section added.
(NORM.DIST returns cumulative distribution for True and Probability mass function for False). Refer here.
3. If a person wants to score 80 percentile based on the sample distribution shared, what should be the score in the test? (76.874) Revised this question.
A Math and Verbal test had the following normal distribution. Math N (69, 19) and Verbal N (75,9). Answer the following questions based on the data shared. What’s the mean and standard deviation of the two mentioned distribution?
For more practice refer to the worksheet second here.
In an attempt to prevent Malaria, a non-profit distributes mosquito nets in a village. Consider this an intervention and a project . The village is under threat of contacting Malaria from other villages as the epidemic is spreading.
Take the prevention of Malaria as a success for this intervention.
After the project is over, the estimate that households don’t have Malaria is 62%. Not having Malaria in a trial is a success. Answer the following questions below.
(Assume that the village never had any mosquito nets and all households received free mosquito nets, and all of them used them during the time of the intervention. Further, there was no case of Malaria among the sampled people both in the control and treatment group before this intervention. During this time Malaria spread from other villages to the present village. Finally, assume that the selection of people is independent and identically distributed. )
(To solve this work problems, you need to have a basic understanding of probability esp. independent events apart from Bernoulli Distribution. Probabilities of independent events are multiplied. Part 3 of the above question is with reference to the Normal Distribution )