Math Answers

An educational researcher found that the average entrance core of the incoming freshmen in a university is 84. A random sample of 24 students from a public school was then selected and found out that their average score in the entrance exam is 88 with a standard deviation of 16. Is there any evidence to show that the sample students from public school performed better than the rest in the entrance examination using the 0.01 level of significance?

A random sample is drawn from a population of known standard deviation 22.1. Construct a 95% confidence interval for the population mean based on the information given (not all of the information given need be used).

a. n=121, x¯=82.4, s=21.9 n=121, x¯=82.4, s=21.9

b. n=81, x¯=82.4, s=21.9 n=81, x¯=82.4, s=21.9

A random sample is drawn from a population of known standard deviation 11.3. Construct 90%confidence interval for the population mean based on the information given (not all of the information given need be used).

a. n=36, x¯=105.2, s=11.2n=36, x¯=105.2, s=11.2

b. n=100, x¯=105.2, s=11.2n=100, x¯=105.2, s=11.2

1.Find the area of the region that lies inside the circle r =3sinx and outside the cardioid

r = 1+sinx

Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} be relations from {1, 2, 3} to {1, 2, 3, 4}. Find R1 − R2

5.6 Assessment Task

Directions. Answer the following items. You may use online calculators and solvers in answering.

1. For each of the following data sets determine the mean:

a. 72, 14,8, 11,57,54,31, 11,67,11,19,3,66 b. 63,9,87,16, 2, 96,13,67,34

c. 1,6,8,2,7,2,9,4,8,9,8,6 d. 12, 0,4,5,8, 3,6, 35,47

e. 2, 7, 17, 33, 67,73, 88, 33, 92, 57,33

2. For each of the following data sets determine the median:

a. 48, 78, 10, 66, 45, 57,96,67, 40, 66, 63,8, 20 b. 28, 3, 10, 60, 8, 23, 45, 97,11, 10

c. 6,9,1, 6, 4, 8, 1, 7, 8, 3, 1, 0

d. 63, 9, 86, 16, 2, 97,24, 67, 34,40 e. 8, 4, 64, 99, 11, 42, 15,88, 54, 77,42

3. For each of the following data sets determine the mode:

a. 98, 37,5,33, 96, 67, 43, 33, 91, 33,32,8,11 b. 104, 2, 51,31,8, 101, 104, 18,47

c. 3, 4, 5, 3,9,8,5,7,2,5,1

d. 19, 1,9,6,4,2,13,15,24,2

e. 8,9,39,44,55,90,19,44,28,69,44

43/76

Solve the following recurrence relation

a) T(n)=T(n-1) +1,for n>2 and T(1)=1

ACTIVITY 8. APPLYING HYPOTHESIS TESTING

Solve the problem:

A recent survey says that Filipino children spend an average of 4 hr a day playing online games with a standard deviation of 30 minutes. A random sample of 9 children is taken from a normally distributed population of children who spend an average of 4 hr and 30 min playing online games. Using the 1% level of significance, would you conclude that the statement given in the survey is correct?

2. A manufacturer of isopropyl alcohol claims that their product has a mean content of 480 mL. and a standard deviation of 21.5 mL. Assume that the variable is normally distributed. a. If a sample is selected, what is the probability that the content will be less than 505 mL? b. If a sample of 6 isopropyl alcohol is selected, what is the probability that the mean of the sample will be less than 505?

If f(x)=(x+1)/x, x ≠ 0 and g(x)= 2x+3, find g°f(x)