Assume a hypothetical survey reports that the average number of articles published over a 5 year period in referred academic journals by faculty at 4 year liberal arts colleges nationwide is 3.2. The faculty at almost Ivy college publish an average of 3.7 articles during that same 5 year period, with a standard deviation (using n-1) of .80. There are 60 faculty at almost Ivy

The probability distribution of the random variable x represents the number of hits a baseball player obtained in a game for the 2012 baseball season. x 0 1 2 3 4 5 upper p left parenthesis x right parenthesisp(x) 0.16740.1674 0.32610.3261 0.29310.2931 0.14880.1488 0.03820.0382 0.02640.0264 the probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). the number of hits was recorded. approximate the mean and standard deviation of the random variable x based on the simulation. the simulation was repeated by performing 50 repetitions of the experiment. approximate the mean and standard deviation of the random variable. compare your results to the theoretical mean and standard deviation. what property is being illustrated? click the icon to view the data tables. compute the theoretical mean of the random variable x for the given probability distribution. mu subscript upper xμxequals=1.6441.644 hits (round to three decimal places as needed.) compute the theoretical standard deviation of the random variable x for the given probability distribution. sigma subscript upper xσxequals=1.1871.187 hits (round to three decimal places as needed.) approximate the mean of the random variable x based on the simulation for 25 games. x overbarxalmost equals≈0.7870.787 hits (round to three decimal places as needed.)