The below table lists the last digits of the 73 published distances (in feet) of the 73 home runs hit by Barry Bonds in 2001 when he set the record for the most home runs in a season (based on data form USA today) The last digit of a data set can sometimes be used to determine whether the data have been measured or simply reported. The presence of disproportionately more 0 s and 5 s is often a indicator that the data have been reported instead of measured.
a) find the mean and standard deviation of those last digit
b) construct the relative frequency table that corresponds to the given frequency table.
c) Construct a table for the probability distribution of randomly selected digits that are equally likely. List the values of the random variables x (0,1,2.....9) along with their corresponding probabilities (0.1, 0.1, .........0.1) then find the mean and standard deviation of this probability distribution.
d) Recognizing that sample data naturally deviate form the results we theoretically expect does it seem that the given last digits roughly agree with the distribution we expect with random selection? Or does it seem that there is something about the sample data (such as disproportionately more 0s and 5s) suggesting that the given last digits are not random?
The Environmental Protection Agency used a tailpipe test to determine which of 116,667 cars generated too much pollution . It is estimated that 1% of cars fail such a test
a) if we randomly select 20 cars from the group of 116,667 how many are expected to fail the tailpipe test?
b) find the mean and standard deviation for the numbers of each of cars in groups of 20 that fail the tailpipe test.
c) find the probability that in a randomly selected group of 20 cars there is at least one that fails the tailpipe test.
d)is it unusual to find that in a group of 20 randomly selected cars there are 3 that fail the tailpipe test? Why or why not?
e) if two different cars are randomly selected find the probability that they both fail the tailpipe test
The solution finds the mean and standard deviation of the number of home runs hit by Barry Bonds in 2001. The relative frequency table is constructed.