Two students attending an exam. Let Si be the event of student i passes an exam. S1 and S2 may or may not be independent of each other. Let random variable X be total number of students who pass the exam. P(S1) = P(S2) = 2/3. X = 0, 1, 2.

1) E(X)

2) What is the min and max of var(X)

An instructor gives a 100-point test in which the grades are approximately normally distributed. The mean is 65 points and the standard deviation is 12 points.

a. What is the lowest possible score to qualify in the top 5% of the scores?

b. If 500 students took the test, how many students received a score between 60 and 80 points?

( I hope the solution to the questions can be provided as well )

Manual Transmission Automobiles In a recent year,

6%

of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of

126

cars,

28

had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with

90%

confidence. Round intermediate and final answers to at least three decimal places.

Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 21 of 42 at one school and 15 of 35 at the other had this infection. Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other. Find the test statistic.

Below you see how many men and women studied sociology and political science.

Give the p-value associated with the test statistic that indicates whether the proportion of female students in political science is smaller than the proportion of female students in sociology. Please round all values to 5 decimal points.

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 91 words per minute​ (wpm) and a standard deviation of 10 wpm.

Complete parts​ (a)

What is the probability that a random sample of 26 second grade students from the city results in a mean reading rate of more than 95 words per​ minute? The probability is _________ ​(Round to four decimal places as​ needed.)

A national health organization warns that 30% of middle school students nation wide have been drunk. A local health agency randomly surveys 100 students and only 25 report having been drunk. Construct an appropriate 80% confidence interval.

A. 0.25

B. 0.0555

C. 0.1946 to 0.3055

D. 0.1651 to 0.3349

Please show work and exaplain why. Thank you!

26% of all college students major in STEM (Science, Technology, Engineering, and Math). If 44 college students are randomly selected, find the probability that a. Exactly 9 of them major in STEM. Incorrect b. At most 14 of them major in STEM. Incorrect c. At least 9 of them major in STEM. Incorrect d. Between 7 and 13 (including 7 and 13) of them major in STEM.

You are invited to give a talk to SPM students who wish to choose their future career in engineering field. As a young engineer graduated from UPNM, you are being selected to give a short introductory speech on the profession of Mechanical Engineer to the students. Write a short outline of the speech which should cover the following topics; explanation of engineering, mechanical engineering, profession, professionalism, attributes and their roles to the society.