Math Answers

A machine produces bolts which are N(4,0.09) where measurements are in cm. Bolts are measured accurately and any bolt smaller than 3.5cm or longer than 4.4cm is rejected. out of 500 bolts how many would be accepted?

Give an example of a function of two variables such that f(0, 0) = 0 but f is NOT continuous at (0, 0). Explain why the function f is NOT continuous at (0, 0).

List the quadruples in the relation { a,b,c,d} where a, b, c, d are integers with

0 < a < b < c < d < 8.

Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0,1),(1, 1), (1, 2), (2, 0), (2, 2) and (3, 0). Find the

(i) reflexive closure of R, (ii) symmetric closure of R

A JKUAT messenger is asked to deliver 10 out of 16 letters to the head of department’s office and the remaining to the dean’s office. He gets confused and on arrival to the dean’s office delivers 10 letters at random to the office. What is the probability that only 6 of the letters to be delivered to the dean’s office actually arrive there?

a)     An insurance company attends 50 clients a day. On average 3 in 100 require special services. On a certain day it is found that there are 3 special service providers available. Assuming that 50 clients will be attended to, find the probability that there are more than three clients require special services?                                                 

Draw the directed graph that represents the relation {(a,a), (a, b), (b, c), (c, d), (a, d), (b, d), (d, b)}.

Suppose a recurrence relation

an=2an−1−an−2

where a1=7 and a2=10

can be represented in explicit formula, either as:

Formula 1:

an=pxn+qnxn

       or  

Formula 2:

an=pxn+qyn

where 

x

and

y

are roots of the characteristic equation.

  Determine p and q

professional basketball player makes 85% of the free throws he tries. Assuming this percentage will hold true for all future attempts, find the probability that in the next eight attempts, the number of free throws he will make is

i. exactly 8 [4 marks]

ii. less than 3 [4 marks]

b) A survey indicates that people use their cellular phones an average of 1.5 years before buying a new one.The standard deviation is 0.25 year. A cellular phone user is selected at random. Find the probability that the user will use their current phone for less than 1 year before buying a new one.[ Assume that the times ( X years) are normally distrbuted]. [4 marks]

The amounts of time it takes for a student to complete a statistics quiz uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events.

a) the student requires more than 55 minutes to complete quiz

b) the student completes the quiz in a time between 30 and 40 minutes

c) the student completes the quiz in exactly 37.23 minutes