Question

How to do this in ti84 plus calculator in shortest possible way

The annual per capita consumption of bottled water was 32.8 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.8 and a standard deviation of 10 gallons.

a. What is the probability that someone consumed more than 43 gallons of bottled​ water?

b. What is the probability that someone consumed between 30 and 40 gallons of bottled​ water?

c. What is the probability that someone consumed less than 30 gallons of bottled​ water?

d. 97.5% of people consumed less than how many gallons of bottled​ water?

Answer 1

Mean = = 32.8

Standard deviation = = 10

By using the Ti-84 plus calculator we have to find probabilities.

a)

We have to find the probability that someone consumed more than 43 gallons of bottled​ water.

That is we have to find P(X > 43)

Click on 2ND ----------> VARS -------> normalcdf( ----------->  

lower: 43

upper: 100000

: 32.8

: 10

Click on Paste option.

We get P(X > 43) = 0.1539

b)

We have to find the probability that someone consumed between 30 and 40 gallons of bottled​ water.

That is we have to find P(30 < X < 40)

Click on 2ND ----------> VARS -------> normalcdf( ----------->  

lower: 30

upper: 40

: 32.8

: 10

Click on Paste option.

We get P( 30 < X < 40) = 0.3745

c)

We have to find the probability that someone consumed less than 30 gallons of bottled​ water.

That is we have to find P(X < 30)

Click on 2ND ----------> VARS -------> normalcdf( ----------->  

lower: -1000000

upper: 30

: 32.8

: 10

Click on Paste option.

We get P( X < 30) = 0.3897

d)

We have given P(X < x) = 0.975

We have to find value of x.

Click on 2ND ----------> VARS -------> invNorm( ----------->  

area: 0.975

: 32.8

: 10

Click on the Paste option.

We get x = 52.40