Math Answers

Find the general solution of the following differential equations using D-operator methods:

(D^2 - 9)y = e^3x + sinx

Solve the following by applying the concepts of percentiles under the normal curve. Show complete solution and draw the normal curve.

1.In a National Achievement Test, the mean was found to be 75 and the standard deviation was 15. The scores also approximate the normal distribution.

a. What is the minimum score that belongs to the upper 15% of the group? (w/ illustration)

b. What is the two extreme scores outside of which 15% of the group are expected to fall?(w/ illustration)

c. What is the score that divide the distribution into two such that 75% of the cases below it?(w/ illustration)

d. Estimate the range of scores that will include the middle 45% of the distribution. (w/ illustration)

2.Scores on the SAT form a normal distribution with a mean score of 500 and a standard deviation of 100.

a. What is the minimum score necessary to be in the top 15% of the SAT distribution?

b. Find the range of scores that defines the middle 80% of the distribution of SAT scores.

Q2. Estimate kurtosis.

  X                   Frequency

1 – 5                   12

5 – 10                11

10 – 15              10

15 – 20               4

20 – 25               3

Q1. Define kurtosis. If β1=1 and β2 =4 and variance = 9, find the values of β3 and β4 and comment upon the nature of the distribution.