According to data360org in 2002 the average water...

According to Data360.org, in 2002, the average water consumption per capita in Japan for the year was 93.5 gallons. Assume that the water the water consumption per capita in Japan follows a normal and symmetrical distribution with a mean of 93.5 gallons and a standard deviation of 12 gallons. Find the following, a. The probability that a person in Japan consumed more than 32 gallons in 2002 b. The probability that a person in Japan consumed between 15 and 25 gallons of water in 2002. c. The probability that a person in Japan consumed less than 15 gallons of water in 2002 d. 90% of the people in Japan consumed more than how many gallons of water.

Transcript

00:01 Distribution that has a mean of 93 .5 and a standard deviation of 12 and we want to find the following probabilities.

00:11 The first thing i'm going to do is get the z -score for each one of these values.

00:15 So i'm going to do it for 32, 15, 25.

00:20 Those are our three values that we're looking at.

00:22 Oh yeah 15 to 25 make sure i got them all.

00:25 So that means we're going to go 32 minus our mean which is 32 .5.

00:29 That doesn't look right.

00:30 Let me look at that mean again.

00:34 90.

00:34 Normal.

00:36 Distribute over 12 and then we're going to have 15 minus 92 .5 over 12 and then we're going to have 25 minus 92 .5 over 12.

00:48 So let's see that's going to be 32 minus 92 .5 and divide that by 12 we get a value of i knew that didn't look right.

00:59 Let me go check these numbers.

01:00 Normal.

01:01 Distribute.

01:02 Oh let's see negative 5 .04.

01:04 Here we're going to go 15 minus oops minus 92 .5, 93 .5 and then divide that by 12 that's going to be negative 6 .54 and then 25 minus 93 .5 divide that by 12 and we get negative 5 .7.

01:26 Now these are very very large z -scores.

01:32 Normal.

01:32 Distribute.

01:34 Calculator instead of a table to get these values.

01:37 So i'm going to go to the normal distribution for this one and i'm going to put to put up with that in my calculator i get this very small number 6 .579923117 times 10 to the negative 8.

01:50 So now i need to subtract that from 1 and i won't get 0 .9999.

01:56 Actually more nines than that...

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