SHOW WORK!!!!! Full credit will not be givenfor answers only. NOTE: for any question asking you to determine aprobability----you MUST write out a probability statement usingproper notation!!!! Probabilities should be DECIMAL form androunded to 4 decimal places.

A company manufactures windows that are inserted intoautomobiles. Each window has five studs for attaching it. A pullouttest is used to determine the force required to pull a stud out ofa window (i.e. Destructive testing). Let F be the force requiredfor pulling studs out of position. Thirty observations of F were asfollows:

159 156 165 142 160 167
151 160 158 148 165 137
161 147 167 158 151 155
120 140 149 160 157 150
137 138 155 144 147 164

NOTE: you can copy and paste the data set intoExcel to make it easier to work with. It is acceptable to use exceland summarize the equations/steps used on your homework paper.

a) Create a stem-and-leaf plot.
b) Calculate the sample mean and sample variance.
c) Determine the 5-number summary.
d) Do any outliers exist in our data? If so, identify them andmathematically justify your answer.
e) Construct a well-labeled modified boxplot.
f) Find the 78th percentile.
g) Does the data set appear to be skewed or symmetric? If it isskewed, decide in what direction. Explain your answer.