Math Answers

A manufacturer of ball pens claims that a certain pen they manufactures has a mean writing life of 400 pages. A purchasing agent selects a sample of 100 pens and puts them for test. The mean writing life from the sample was 390 pages with a standard deviation of 30 at alpha 0.01.

The hypotenuse of a right triangle is constantly 8 inches long. One leg is increasing at the

rate of 3in./min. At what rate is the area of the triangle changing when the increasing leg is

4in.

Is this statement true or false ? provide reason for your answer 

d/dx[ _x²∫(π/2) e^2cost dt ] = -2xe^{2(cosx^2)}

 if I_n = ₀∫∞ e^-xsinⁿ(x)dx , prove that (1+n²)I_n = n(n-1) I_n-2 for n >₌ 2

if f(x) = sin^-1x , show that ( 1-x²) f^'' (x) -x f^'(x) = 0 . Hence prove that , f⁽ⁿ⁺²⁾(0) = n² fⁿ (0)

A school teacher suspects the claim that the mean number of students that use library materials in a certain school is at most 450. To check the claim, the professor checks a random sample of 100 library records and obtain that the mean number of students using library materials is 458 with a standard deviation of 9. What would be the teacher's conclusion using 0.05 level of significance?

a. State the null and alternative hypothesis in symbols.

b. Choose the test statistic applied where 𝛼 = 0.05

c. Determine the critical points

d. Computation of the test statistic

e. Decision

f. Conclusion

Bhartdarshan’ is an Internet-based travel agency wherein customers can see videos of the

cities they plan to visit. The number of hits daily is a normally distributed random variable

with a mean of 10,000 and a standard deviation of 2,400.

a. What is the probability of getting more than 12,000 hits?

b. What is the probability of getting fewer than 9,000 hits?

Scores on a scholarship aptitude exam are normally distributed with a mean of 72 and a standard deviation of 8. What is the lowest score that will place an applicant at the top 10% of the distribution?

A division wide aptitude test in mathematics was conducted to 1000 pupils. The mean of the test is 58 and the standard deviation is 12. The scores also approximate the normal distribution. What is the minimum score to belong the upper 20% of the group?

1. Directions: Determine each of the following areas and show these graphically. Use probability notation in your final answer. NOTE: Use graphing paper to graph.

1. To the left of z = 1.96 5. Below z = -1.96       9. 1.27≥z≥-2.1

2. At most z = 2.58 6. z≥1       10. z=-0.58

3. At least z = 1.96 7. z≤-1.5

4. To the right of z = 0.33 8. -0.92≤z≤1.75