Question

In: Statistics and Probability

A statistics class for engineers consists of 53 students. The students in the class are classified...

A statistics class for engineers consists of 53 students. The students in the class are classified based on their college major and sex as shown in the following contingency table:

	College Major
Sex	Industrial Engineering	Mechanical Engineering	Electrical Engineering	Civil Engineering	Total
Male	15	6	7	2	30
Female	10	4	3	6	23
Total	25	10	10	8	53

If a student is selected at random from the class by the instructor to answer a question, find the following probabilities. Report your answer to 4 decimal places. (total 80 points)

Consider the following events:

A: The selected student is a male.

B: The selected student is industrial engineering major.

C: The selected student is civil engineering major.

D: The selected student is electrical engineering major.

Note: Indicate the type of probability as marginal, joint or conditional when asked.

Find the probability that the randomly selected student is a male. Indicate the type of probability. (8 + 2 = 10 points)

Find the probability that the randomly selected student is industrial engineering major. Indicate the type of probability. (8 + 2 = 10 points)

Find the probability that the randomly selected student is male industrial engineering major. Indicate the type of probability. (8 + 2 = 10 points)

Given that the selected student is industrial engineering major, what is the probability that the student is male? Indicate the type of probability.

(8 + 2 = 10 points)

Based on your answers on part a and d, are sex and college major of students in this class independent? Provide a mathematical argument? (6 points)

Consider the events A and B. Are sex and college major mutually exclusive events? Provide a mathematical argument to justify your answer. (6 points)

Find the probability that the randomly selected student is male or industrial engineering college major. (10 points)

Consider the events C and D. Are college major mutually exclusive events? Provide a mathematical argument to justify your answer. (6 points)

Find the probability that the randomly selected student is civil or electrical engineering college major. (6 points)

What is the probability that a randomly selected student is neither a male nor an industrial engineering college major? (6 points)

Expert Solution

For further queries, please comment below.

Thank you.

orchestra answered 2 years ago

In a large introductory statistics lecture hall, the professor reports that 53% of the students enrolled...

In a large introductory statistics lecture hall, the professor reports that 53% of the students enrolled have never taken a calculus course, 28% have taken only one semester of calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. You are assigned to be part of a group. What is the probability that of your other two groupmates, a) neither has...

Consider a population that consists of the 70 students enrolled in a statistics course at a...

Consider a population that consists of the 70 students enrolled in a statistics course at a large university. If the university registrar were to compile the grade point averages (GPAs) of all 70 students in the course and compute their average, the result would be a mean GPA of 2.98. Note that this average is unknown to anyone; to collect the GPA information would violate the confidentiality of the students’ academic records. Suppose that the professor who teaches the course...

The failure rate in a statistics class is 20%. In a class of 30 students, find...

The failure rate in a statistics class is 20%. In a class of 30 students, find the probability that exactly five students will fail. Use the normal distribution to approximate the binomial distribution.

The 90 students in a statistics class are categorized by gender and by the year in...

The 90 students in a statistics class are categorized by gender and by the year in school. The numbers are listed in the following table: Year in School Freshman Sophmore Junior Senior Gender Male 1 4 8 17 Female 23 17 13 7 Test the null hypothesis that there is no association between the year in school and the gender using a 1% significance level. Be sure to specify the test statistic with degrees of freedom, the P-value or critical...

In an introductory statistics class, there are 18 male and 22 female students. Two students are...

In an introductory statistics class, there are 18 male and 22 female students. Two students are randomly selected (without replacement). (a) Find the probability that the first is female (b) Find the probability that the first is female and the second is male. (c) Find the probability that at least one is female --------------- I know that this question has to use the counting method, but i got confuse with how to start because i have to now find the...

A: You recently took a statistics class in a large class with n = 500 students....

A: You recently took a statistics class in a large class with n = 500 students. The instructor tells the class that the scores were Normally distributed, with a mean of 7 2 (out of 100 ) and a standard deviation of 8 , but when you talk to other students in the class, you find out that more than 30 students have scores below 45 . That violates which rule for the Normal distribution? the 30–60–90 rule the 1–2–3...

Statistics grades: In a statistics class of 47 students, there were 17 men and 30 women....

Statistics grades: In a statistics class of 47 students, there were 17 men and 30 women. Three of the men and four of the women received an A in the course. A student is chosen at random from the class. (a) Find the probability that the student is a woman. (b) Find the probability that the student received an A. (c) Find the probability that the student is a woman or received an A. (d) Find the probability that the...

Statistics Class Times A professor wishes to see if students show a time preference for statistics...

Statistics Class Times A professor wishes to see if students show a time preference for statistics classes. A sample of four statistics classes shows the enrollment. At =α0.01, do the students show a time preference for the classes? Use the P-value method with a TI-83 Plus/TI-84 Plus calculator. Time :800AM :1000AM :1200PM :200PM Students 22 35 29 26

Question 3: A freshman class consists of 6 students, 3 of which are girls. The class...

Question 3: A freshman class consists of 6 students, 3 of which are girls. The class needs to select a committee of 2 to represent them in the student senate. (1) Write the sample space of this experiment. (2) Calculate the probability of a committee of two boys. (3) Calculate the probability of one boy and one girl.

There are 46 students in an elementary statistics class. On the basis of years of experience,...

There are 46 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 4 min. (Round your answers to four decimal places.)(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is...