Math Answers

There are 150 students in a class. The distribution if their marks in a mathematics test are as follows

Class                                                   frequency

0-9                                                      3

10-19                                                  10

20-29                                                  17

30-39                                                  x

40-49                                                  35

50-59                                                  y

60-69                                                  18

70-79                                                  10

80-89                                                  5

90-99                                                  2

Required

i)       The value of x given that the median mark is 44.357            (2marks)

ii)     The value of y given that the modal is 43.0                          (2marks)

iii)   Draw an ogive of the data in (a) above                                 (3 marks)

Solve

x^2y′′+ xy′− y =1/x + 1

Solve

x ^2y'′ + 2xy'− 12y = x^3log x.

8. Solve x

x^2y′′− 2xy′+ 2y = x^4sin(4 log x)

•Construct the truth table of the converse,

contrapositive, and inverse of p→ q

•Let p, q, and r be propositions. Construct the

truth table of r→(˥p⋀q)

The probability density function for a diameter of a drilled hole in millimeters is f(x) = 10e^-10(x-5) for x > 5 mm. Although the target diameter is 5 mm, vibrations, tool wear, and other nuisances produce diameters larger than 5 mm.

a) Determine the mean and variance of the diameter of the holes. [Hint: Use integration by parts.]

b) Determine the probability that the hole exceeds 5.1 mm.

Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, which is probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful is $10 million, $5 million, and $1 million, respectively. Let the random variable X denote the yearly revenue of the product. Determine:

a) the mass function of X;

b) the mean of X; and

c) the variance of X.

1000 students took an examination in Statistics and Probability. The mean score obtained is 71 and the standard deviation is 4. Assuming that the data are normally distributed, find the area and probability of students who obtained a score of:

a. at least 83

b. mean to 92

c. at most 70