How much oil wells in a given field will ultimately produce is key information in deciding whether to drill more wells. Data was
collected estimating the total amount of oil recovered (in thousands of barrels) from 64 wells in the Devonian Richmond Dolomite area of the Michigan Basin. The data is in an Excel file on Canvas. Give a 95% confidence interval for the mean amount of oil recovered from all wells in this area.
DATA:
Oil
21.7
53.2
46.4
42.7
50.4
97.7
103.1
51.9
43.4
69.5
156.5
34.6
37.9
12.9
2.5
31.4
79.5
26.9
18.5
14.7
32.9
196
24.9
118.2
82.2
35.1
47.6
54.2
63.1
69.8
57.4
65.6
56.4
49.4
44.9
34.6
92.2
37
58.8
21.3
36.6
64.9
14.8
17.6
29.1
61.4
38.6
32.5
12
28.3
204.9
44.5
10.3
37.7
33.7
81.1
12.1
20.1
30.5
7.1
10.1
18
3
2
DATA:
Oil
21.7
53.2
46.4
42.7
50.4
97.7
103.1
51.9
43.4
69.5
156.5
34.6
37.9
12.9
2.5
31.4
79.5
26.9
18.5
14.7
32.9
196
24.9
118.2
82.2
35.1
47.6
54.2
63.1
69.8
57.4
65.6
56.4
49.4
44.9
34.6
92.2
37
58.8
21.3
36.6
64.9
14.8
17.6
29.1
61.4
38.6
32.5
12
28.3
204.9
44.5
10.3
37.7
33.7
81.1
12.1
20.1
30.5
7.1
10.1
18
3
2
1 answer:
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Answer:
0% probability that at least 1,500 will agree to respond
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the probability that at least 1,500 will agree to respond
This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So
has a pvalue of 1.
1 - 1 = 0
0% probability that at least 1,500 will agree to respond