An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.

P(High- quality oil) = 0.3

P(medium - quality oil)=0.4

P (no oil)= 0.3

a. What is the probability of finding oil (to 1 decimal)?

b. After feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below.

P(Soil /High- quality oil) = 0.4

P(Soil/medium - quality oil)=0.4

P (Soil/no oil)= 0.2

Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).

P(Soil /High- quality oil) = ?

P(Soil/medium - quality oil)= ?

P (Soil/no oil)= ?

c. What is the new probability of finding oil (to 4 decimals)?

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above