Which of the following is most likely to be approximately normally distributed?
ID: 3222478 • Letter: W
Question
Which of the following is most likely to be approximately normally distributed? (A) The scores on a very easy 5-question mental math quiz taken by a large number of students (B) The scores on a large number of rolls of a cube whose faces are numbered 1 through 6 (C) The number of attempts it took to pass the drivers' test for the population of drivers in New York State (D) The tail lengths of fully grown males of the common raccoon species (E) The responses to a survey question given to a large number of people where the possible responses were "yes, " "no, " and "maybe"Explanation / Answer
Answer to the question)
a) ths is not a normal distribution, because the questions are all easy type , this will lead to more higher scores. and hence the distribution would be skewed
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b) The cube has 4 outcomes, and since nothing is mentioned we consider them all to be equally likely , thus the probability distribution would be uniform and discrete for this particular expeirment. Hence it would not be normal distribution
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c) The number of attempts may be very less for very few people, it would be average for most of the peopl and again the number of attempts would be very high for very few people, thus this particular variable follows Normal distribution
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d) The tail length of fully grown males would again get a skewed data
had it been that the data related to only tail length of the entire species, there would have been normal distribution , but because here the reference is to the "fully grown males" hence we would get all the higher tail lengths and this will cause the data to skew. Thus it woud not be a normal distribution.
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e) The responses to the survey are categorical data , with ordinal scale of measurement, thus this data would not follow normal distribution
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