1) The following sample of data represents the scores of 20 students on an engineering examination

1) The following sample of data represents the scores of 20 students on an engineering examination. The mean is 70.2, and the standard deviation is 18.5. 70, 39, 51, 63, 59, 68, 69, 75, 73, 78, 77, 80, 82, 88, 89, 85, 90, 15, 67, 86.    (a). Calculate the z-scores of the lowest and highest grades.    (b). Based on the above values, are there any outliers in the data set?

2) Consider the following car mileages of randomly selected 9 cars. 33.5 33.0 35.6 30.7 36.3 31.5 25.0 33.2 35.0 40.5 Using the z-scores of the above values, check for the availability of outliers.

3) Consider the following sample of data, which represents the pitching speed (miles per hour) of pitchers in 20 games of a major baseball league. 85, 90, 95, 88, 92, 91, 87, 89, 86, 92, 80, 70, 75, 68, 69, 74, 77, 80, 75, 73.     (a)Construct a stem-and-leaf plot for the above data.   (b). Calculate the 70th and 80th percentiles for the above data.    (c). Interpret the above percentiles.