Area of Study Probability Engineering 0154 Physical sciences

Area of Study Probability Engineering 0.154 Physical sciences 0.087 Life sciences 0.203 Mathematics 0.031 Computer sciences 0.033 Social sciences _____ 0.168 Humanities 0.094 Education _____ 0.132 Professional and other fields 0.056 Health 0.042 Source: U.S. National Science Foundation (a) Verify that this is a probability model. (b) What is the probability that a randomly selected doctoral candidate who earned a degree in 2009 studied physical science or life science? Interpret this probability. (c) What is the probability that a randomly selected doctoral candidate who earned a degree in 2009 studied physical science, life science, mathematics, or Computer science? Interpret this probability. (d) What is the probability that a randomly selected doctoral candidate who earned a degree in 2009 did not study mathematics? Interpret this probability. (e) Are doctoral degrees in mathematics unusual? Does this result surprise you?

Solution

a) The sum of all the individual probabilities for area of study is 1.0

Hence this is a probability model

b) Probability(Physical Science) + Probability(Life Science) = 0.087 + 0.203 = 0.290

This implies that out of every 1000 students 290 would earn a degree in either Physical Science or Life Science

c) Probability(Physical Science) + Probability(Life Science) + Probability(Mathematics) + Probability(Computer Science) = 0.087 + 0.203 + 0.031 + 0.033 = 0.354

This implies that out of every 1000 students 354 would earn a degree in either Physical Science, Life Science, Mathemartics or Computer Science

d) Probability(Mathematics) = 0.031

Probability(Did not study Mathematics) = 1 - 0.031 = 0.969

This implies that out of every 1000 students 969 did not study Mathemartics

e) Yes doctorate degrees in Maths are unusual due to the least probability assigned to it - 0.031

These results do not surprise as this is as per the norm