00:01
So, as per the question, we are going to use the empirical rule and estimate the percentage of usage.
00:06
So, part a, the probability should range in between 16 .4 to 21 .2 gallons.
00:16
So, that is going to be given as probability 16 minus 4 minus the mean value which is 18 .8.
00:25
So, we will write since mu is equal to 18 .8 and sigma standard deviation is 2 .4 minus 18 .8 over 2 .4 should be less than z value rather we can write x minus 18 .8 that is mu over sigma.
00:51
So, 2 .4 should be less than 21 .2 minus 18 .8 over 2 .4.
00:59
So, that will be probability of z less than 1 minus probability of z less than minus 1.
01:07
So, using z score table, we are going to have the value as 68 percent for part a.
01:20
Now, for part b, we are going to have probability of x greater than 26 gallons.
01:26
This is 1 minus probability of x minus mu 18 .8 over sigma 2 .4 should be less than 26 minus 18 .8 over 2 .4...