1.) Find the following areas under the standard normal curve.

a. The area to the left of z = -0.76

b. The area to the right of z = -1.36

c. The area between z = -1.22 and z = 1.33

2.) A large group of students took a test in Finite Math where the grades had a mean of 75 and a standard deviation of 4. Assume that the distribution of these grades is approximated by a normal distribution, and that passing the test is a 65.

a. What percent of students scored higher an 80 or higher?

b.What percent of students failed the test?

c.) What happens when you try to find the percent of students that scored less than a 40?

In a high school orchestra there are 3 training groups: one is Violin, one in Flute, and one in Cello. These sections are open to any of the 100 students in the school. There are 36 students in the Violin group, 30 in the Flute group, and 27 in the Cello group. There are 9 students that are in both Violin and Flute, 18 that are in both Violin and Cello, and 6 are in both Flute and Cello. In addition, there are 4 students taking all 3 sections. If a student chosen at random,

a) the probability that he is not included in any of these groups is?

b) the probability that he is playing exactly one instrument group is?

c) When two people are chosen randomly, the probability that at least 1 is in an instrument group is?

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 104 cars owned by students had an average age of 5.42 years. A sample of 145 cars owned by faculty had an average age of 5.57 years. Assume that the population standard deviation for cars owned by students is 2.69 years, while the population standard deviation for cars owned by faculty is 2.46 years. Determine the 98% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval.

9.55 The U.S. Department of Education reports that 40% of full-time college students are employed while attending college. (Data extracted from The Condition of Education 2012,ncesed.gov/pubs2012/2012045.pdf.) A recent survey of 60 full-time students at a university found that 25 were employed.

A) Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the proportion of full-time students at the university is different from the national norm of 0.4

B) Assume that the study found that 32 of the 60 full-time students were employed and repeat (a). Are the conclusions the same?

A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 225 students using Method 1 produces a testing average of 68.2 A sample of 242 students using Method 2 produces a testing average of 66.2. Assume that the population standard deviation for Method 1 is 5.66 while the population standard deviation for Method 2 is 10.06. Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2.

Step 3 of 3 :  

Construct the 98% confidence interval. Round your answers to one decimal place.

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 76 cars owned by students had an average age of 8.72 years. A sample of 119 cars owned by faculty had an average age of 8.95 years. Assume that the population standard deviation for cars owned by students is 3.64 years, while the population standard deviation for cars owned by faculty is 3.51 years. Determine the 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 1 of 3 : Find the point estimate for the true difference between the population means

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 217 cars owned by students had an average age of 7.62 years. A sample of 252 cars owned by faculty had an average age of 6.266.26 years. Assume that the population standard deviation for cars owned by students is 2.67 years, while the population standard deviation for cars owned by faculty is 3.41 years. Determine the 99% confidence interval for the difference between the true mean ages for cars owned by students and faculty.

Step 1 of 3 :  

Find the point estimate for the true difference between the population means.

It is estimated that 16% of those taking the quantitative methods portion of the certified public accountant (CPA) examination fail that section. Seventy students are taking the examination this Saturday.

a-1. How many would you expect to fail? (Round the final answer to 2 decimal places.)

Number of students           

a-2. What is the standard deviation? (Round the final answer to 2 decimal places.)

Standard deviation           

b. What is the probability that exactly eight students will fail? (Round the final answer to 4 decimal places.)

Probability           

c. What is the probability at least eight students will fail? (Round the final answer to 4 decimal places.)

Probability           

For any confidence interval make sure that you interpret the interval in context, in addition to using it for inference.

A survey is given to 300 random SCSU students to determine their opinion of being a “Tobacco Free Campus.” Of the 300 students surveyed, 228 were in favor a tobacco free campus.

1. Find a 95% confidence interval for the proportion of all SCSU students in favor of a tobacco free campus.
2. Interpret the interval in part a.
3. Find the error bound of the interval in part a.
4. The Dean claims that at least 70% of all students are in favor of a tobacco free campus. Can you support the Dean’s claim at the 95% confidence level? Justify!

In a high school literature club, there are 3 groups: one is Novel, one in Poetry, and one in Comics. These sections are open to any of the 100 students in the school. There are 25 students in the Novel group, 31 in the Poetry group, and 19 in the Comics group. There are 18 students that are in both Novel and Poetry, 7 that are in both Novel and Comics, and 14 are in both Poetry and Comics. In addition, there are 5 students taking all 3 groups. If a student chosen at random,

a) the probability that he is not included in any of these groups is

b) the probability that he is playing exactly one literature group is

c) When two people are chosen randomly, the probability that at least 1 is included in a group is