60% of all students at a college still need to take another math class. If 49 students are randomly selected, find the probability that

a. Exactly 26 of them need to take another math class.____  
b. At most 31 of them need to take another math class.____   
c. At least 28 of them need to take another math class.____   
d. Between 25 and 31 (including 25 and 31) of them need to take another math class.____  

19. FHSU wants to know if their students tend to drink more coffee than the national average. They ask a random sample of 75 students how many cups of coffee they drink each day and find the average to be 3.8 cups with a standard deviation of 1.5 20. Redo #19, only this time assume the value 1.5 is the population standard deviation. Then, state this interval below within an interpretive sentence tied to the given context. Please explain 20

69% of all students at a college still need to take another math class. If 41 students are randomly selected, find the probability that a. Exactly 30 of them need to take another math class. b. At most 27 of them need to take another math class. c. At least 29 of them need to take another math class. d. Between 23 and 29 (including 23 and 29) of them need to take another math class.

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution. (Source: http://www.ets.org/.) Suppose a random sample of 10 students took the test, and their scores are given below. 152, 126, 146, 149, 152, 164, 139, 134, 145, 136 a) Test the claim that the mean verbal reasoning score is different from 150 at the α = 0.10 level of significance.

A sample of 53 night-school students' ages is obtained in order to estimate the mean age of night-school students. x = 25.5 years. The population variance is 13.

(b) Find the 95% confidence interval for μ. (Give your answer correct to two decimal places.)

(c) Find the 99% confidence interval for μ. (Give your answer correct to two decimal places.)

Students in a biology class have been randomly assigned to one of the two mentors for the laboratory portion of the class. A random sample of final examination scores has been selected from students supervised by each mentor, with the following results:
Mentor A: 78, 78, 71, 89, 80, 93, 73, 76
Mentor B: 74, 81, 65, 73, 80, 63, 71, 64, 50, 80
At the 0.05 significance level, is there a difference in the mean scores?

The following scrabble tiles are poured out and then randomly arranged. E L E E M M O S Y N L G S S

What is the probability that all S tiles are adjacent in your arrangement? b) Eight students are randomly seated in a row. Two students Bert and Ernie hate each other and there must be at least 3 people between them or they will get into a fight. What is the probability a fight is avoided?

A study was designed to measure the effect of home environments on academic achievement of 12 year old students. Because genetic differences may contribute, the researcher controlled for this factor. 30 sets of twins were studied where 1 was in a home where academics were emphasized (Academic) and the other twin was placed in home where it was not emphasized (nonacademic). The final grades for 60 students were measured. Is this example an independent paired t-test or a dependent paired t-test?

A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 81 students, the mean age is found to be 20.51 years. From past studies, the standard deviation of the population is known to be 2 years, and the population is normally distributed. Construct a 99% confidence interval of the population mean age. (Round off final answers to two decimal places, if appropriate. Do not round off numbers taken directly from tables).