Radiologists are often asked to predict the sex of a baby from ultrasound images made during pregnancy. The authors of a paper followed up on 159 predictions made by a particular radiologist (Radiologist 1) to determine whether or not they were correct. Data from the paper is summarized in the following table.
Radiologist 1
Predicted
Male
Predicted
Female
Baby is Male
74
13
Baby is Female
14
58
(a) Assuming that these data are representative of sex predictions made by Radiologist 1, estimate the probability that a sex prediction is correct, given that the baby is male. (Round your answer to three decimal places.)
0.852
x
(b) Assuming that these data are representative of sex predictions made by Radiologist 1, estimate the probability that a sex prediction is correct, given that the baby is female. (Round your answer to three decimal places.)
0.806
(c) For Radiologist 1, is a sex prediction more likely to be correct if the baby is male? Explain.
No, the answer for (a) is less than the answer to (b). The prediction is more likely to be correct when the female.
No, the answer for (a) is greater than the answer to (b). The prediction is more likely to be correct when the female.
Yes, the answer for (a) is greater than the answer to (b). The prediction is more likely to be correct when the male.
Yes, the answer for (a) is less than the answer to (b). The prediction is more likely to be correct when the male.
(d) Estimate the probability that a sex prediction made by Radiologist 1 is correct. (Round your answer to three decimal places.)
0.831
x