Question

Physical Sciences. Hydraulic fracturing, or fracking, is a method used to extract natural gas from deep shale deposits. This process involves over 500 chemicals and millions of gallons of water. In a random sample of fracking wells, the mean depth was 8000 feet. Assume the standard deviation is 440 feet and the distribution of depths is approximately normal. (a) What proportion (±±0.01) of wells have depths between 7120 and 8880 feet? (b) What proportion (±±0.0001) of wells have depths less than 6680 feet? (c) What proportion (±±0.0001) of wells have depths between 7560 and 9320 feet? (d) Suppose a new fracking well was drilled in 2012 to a depth of 8255 . Is there any evidence to suggest that the mean depth of wells has changed? zz(±±0.0001) = Conclusion: There is evidence There is no evidence.

Can someone please explain how to do this on a TI-84?

Answer 1

Solution:

   We are given that : In a random sample of fracking wells, the mean depth was 8000 feet. Assume the standard deviation is 440 feet and the distribution of depths is approximately normal.

That is :    and Standard Deviation =

Part a) hat proportion (±±0.01) of wells have depths between 7120 and 8880 feet?

In TI-84 , we use following steps:

1) Press 2ND   

2) Press VARS ( DISTR)

3) Select 2 : normalcdf (

4) Enter the numbers:

Since we have to find probability between 7120 and 8880, Lower = 7120 and Upper = 8880

Thus we enter :

Lower : 7120

Upper : 8880

Paste and press Enter.

which gives answer 0.9545

Part b) What proportion (±±0.0001) of wells have depths less than 6680 feet?

Use same steps used above but Enter following numbers in following way:

Since we have to find Probability less than 6680 , lower limit would be - infinity

Thus we use -10^99 for lower limit. To get - sign , we press (-) button which is at the bottom of calculator.

Thus we get :

Lower : - 10^99

Upper : 6680

Paste and press Enter.

which gives answer 0.0013

Part c) What proportion (±±0.0001) of wells have depths between 7560 and 9320 feet?

Use same steps used in part a)

Lower : 7560

Upper : 9320

Paste and press Enter.

which gives answer 0.8399948 = 0.8400 ( rounded to 4 decimal places )

Part d) Suppose a new fracking well was drilled in 2012 to a depth of 8255 . Is there any evidence to suggest that the mean depth of wells has changed?

Since sample size is not given , we assume n = 1

we use following steps:

1) Press STAT

2) Select TESTS

3) Under TESTS select Z test

4) Under Z test Select Stats

5) Under Stats enter the numbers:

Thus we get following output:

Since z = 0.5795 and p value = 0.5622, we conclude that there is no eveidence to suggest that the mean depth of wells has changed.