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SAMPLE MIDTERM EXAMSTAT 53-10Spring 2006Answer all the questions. Please show full work for partial credit.1)Consider the following data on the number of hits to a Library website on 14randomly picked days:390 406446420370328410320368392280325382290(a)(12 points) Construct a box plot for the above data?(b) (4 points) Is the distribution symmetric? Explain.2)(18 points) The number of passengers in a car on a freeway is a random variablewith the following probability distribution:X12345P(x)0.4-0.150.10.05(a)Find the probability that there are at most two passengers in a car(b) Find the mean number of passengers in a car.(c)Find the probability that the number of passengers in a car is within 1standard deviation from the mean.3)(15 points) A study of the behavior of large number of drug offenders aftertreatment for drug abuse suggests that the likelihood of conviction within a two-year period after treatment may depend on the offender’s education. The