Your job as the research director in the Alabama Department…

 Your job as the research director in the Alabama Department of Youth Services is to advise the Director which policies to follow. In the past, you have heard that some institutions have had as many as 80 disturbances in a year.  The average number of disturbances (riots, stabbings, fights, etc.) per year per institution, though, is 37, with a standard deviation of 6.  The distribution is normal.  Answer the following questions.   a) What is the z-score for an institution that had 40 disturbances in one year?  What does this z-score indicate?   b) You want to give raises to the wardens in the prisons that have disturbances in the bottom 10% of the distribution, and fire the wardens in prisons in the top 10%.  What number of disturbances will be the cut-off for each of these decisions?   c) What is the probability that an institution would have 40 or fewer disturbances?   d) What is the probability that an institution would have 36 or more disturbances?  

Four identical blocks each of mass m are arranged as shown o…

Four identical blocks each of mass m are arranged as shown on a frictionless surface. Block 1 is pushed with a force F. The coefficient of friction between the blocks is large enough that the blocks do not slide with respect to one another (so there is a friction between the blocks but no friction from the horizontal surface). We can neglect drag from the air.  Your friend draws the free body diagram on block 3.  You are asked to evaluate their work and you start by making sure they have the right number of forces. You tell your friend