Probability& The Normal Curve Homework A sociology department at a university co

Question

Probability& The Normal Curve Homework A sociology department at a university collected the following demographic data on its members. Listed are several demographic categories, as well as the proportion of faculty members that fit into each. Assuming that all subcategories within the major categories are mutually exclusive, use the information to answer questions 1 through 6 Category Proportion1. What is the probability of a faculty member being Ethnic background female and having a Ph.D.? 63 16 Caucasian American Hispanic American Asian American African American Other 03 07 2. What is the probability of a faculty member being female and African American? Gender Male Female 65 35 3. What is the probability of a faculty member being a male with a Ph.D. and an "other" ethnicity background? Highest college degree 4. What is the probability of a faculty member being a female? Ph.D M.A. B.A. A.A. 85 10 04 01

Explanation / Answer

Solution:

Step 1 of 5:

Here we are given with a data set regarding the categories of faculty members and their proportions.

Using this data we need to obtain the required values.

Step 2 of 5:

(1).

Here we need to find the probability that a faculty members is a female and Ph.D holder.

It is given that all the events are mutually exclusive.So the required probability becomes

P(female)*P( Ph.D holder)

=(0.35)*(0.85)

=0.2975

Thus, the required probability is 0.2975.

Step 3 of 5:

(2).

Here we need to find the probability that a faculty member is a female and African american.

This probability is given by

P(female)*P(african American)

=(0.35)*(0.03)

=0.0105

Thus, 0.0105 is the probability that the faculty member is a female and African American.

Step 4 of 5:

(3)

Here we need to find the probability that the faculty member is a male having a Ph.d and he is from "other" category.

This probability is given by

P(male)*P(Ph.d)*P(other)

=(0.65)*(0.85)*(0.07)

=0.0387

Thus, 0.0387 is the probability that the faculty member is a male with a Ph.d and he is from other category.

Step 5 of 5:

(4).

Here we need to find the probability that the faculty member is a female.

It is given that the proportion of female is 0.35.

Thus, 0.35 is the probability that the faculty member is a female.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.