1. A five number summary for a data set is given by the minimum, the maximum, th
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Question
1. A five number summary for a data set is given by the minimum, the maximum, the first quartile (Q1), the median, and the third quartile (Q3). Assume that, in a particular data set, we have: Minimum = 39.6 Q1 = 62.7 Median = 71.8 Q3 = 76.8 Maximum = 82.6. Are there any outliers in this data set? Base your conclusion on what we learned this far in the course, and justify your answer.
2. A and B are two mutually exclusive events within the same sample space. If P(A)=1/4 and P(B)=1/8, are the the events A and B independent? Justify!
3. Assume that a particular outcome from a random process has a probability of 0.001. Which of the following statements is true? Justify!
a) The outcome will occur once in every1000 trials, always.
b) The outcome will never happen.
c) The outcome will occur once in 1000 trials, on average.
d) The outcome may or may not happen. The chances for both are equal.
Explanation / Answer
1) as Q3-Q1 =76.8-62.7 =14.1
hence lower tail =Q1 -1.5(Q3-Q1) =62.7-1.5*14.1=41.55
as value below 41.55 is outlier and as minimum value is 39.6 hence there are outliers on lower tail side.
similarly
upper tail =Q3 +1.5(Q3-Q1) =76.8+1.5*14.1 =97.95
as this value is higher then maximum value, hence there is no outlier on upper tail
2) as A and B are mutually exclusive . hence P(AnB) =0
put P(A)*P(B) =(1/4)*(1/8) =1/32
as P(AnB) is not equal to P(A)*P(B) they are not independnet.
3)c) The outcome will occur once in 1000 trials, on average.
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