pix plim °-Am dumatul, uenhe an esti- show that , 5 The following histogram was
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Question
pix plim °-Am dumatul, uenhe an esti- show that , 5 The following histogram was created using the variable score in the data file ECONMATH. Thirty bins were used to create the histogram, and the height of each cell is the proportion of observations falling within the corresponding interval. The best-fitting normal distribution-that is, using the sample mean and sample standard deviation-has been superimposed on the histogram. 08 .06 .04 .02 60 course score (in percentage form) 20 40 80 100 (Gi) If you use the normal distribution to estimate the probability that score exceeds 100, would the answer be zero? Why does your answer contradict the assumption of a normal distribution for score? (ii) Explain what is happening in the left tail of the histogram. Does the normal distribution fit well in the left tail?Explanation / Answer
Solution-
1. If we use normal distribition to calculate probability that score exceeds 100%, answers will not be zero, although it will be very small. This is because right tail will be somewhat above the axis( but close to it) suggesting positive probabilty. This condradicts with the fact that score can not exceed 100% which us due to design of tails under normal distribution.
2. Left tail is perfectly good as it suggests that probabilty of getting score less than 40 or less decreases as we approach towards lesser score. This is what we expect in normal distribution as probabilty attached to outliers are very small.
Answer
TY!
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