3.a. The given table shows the rainfall of Gujarat Region. Forecast the rainfall using Exponential Smoothing. Use Alpha =0.2, 0.5 and 0.8. Data is available from 1997 to 2016, use this series for the calculation and forecast the rainfall for the year 2017. To know, what extent the prediction is correct, actual rainfall for 2017 (1024.4millimeters) is provided. Based on MSE and MAD, find out which alpha values among the three suggestions are relatively near to actual value?

3.b. A new gas-electric hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events. (show the concerned region by z curve)

1. The car travels more than 70 miles per gallon.

2. The car travels less than 60 miles per gallon.

3. The car travels between 55 and 70 miles per gallon.

Kindly answer the 3.b.part

SUBDIVISION YEAR ANNUAL (in MM) Gujarat Region 1997 1068.9 Gujarat Region 1998 1070 Gujarat Region 1999 568.4 Gujarat Region 2000 550.6 Gujarat Region 2001 849 2002 637.2 Gujarat Region Gujarat Region Gujarat Region 2003 1160.3 2004 1005.8 Gujarat Region 2005 1316.4 Gujarat Region 2006 1478 2007 1178.9 Gujarat Region Gujarat Region Gujarat Region 2008 911.1 2009 641.6 2010 1088.7 2011 890.5 Gujarat Region Gujarat Region Gujarat Region Gujarat Region 2012 714 2013 1118.6 Gujarat Region 2014 705.7 Gujarat Region 2015 622.9 Gujarat Region 2016 764.9