Math Answers

Ramdon sample of size 4 are drawn froem the finite population which consists of the number 2,3,7,8 and 10

Find

lim [1/(2n+1)^2

+2/(2n+2)^2+3/(2n+3)^2+..3/25n] n→ ∞

Let X be a random variable that denotes the number of passengers in a train station for a given hour. What are the possible values of X?

1.graph the height of a right triangle as a function of the base ,if the hypotenuse is fixed at 10.

2.graph the diameter of a circle as a function of it's circumstances.

3.determine whether the following function is continuous or discontinuous .

f(x)=3x+2/x^2-6

a.at x =-1

b.at x =-2

Evaluate the integral of sin³ y cos 2y dy from 0 to 𝜋/2.

Evaluate the integral of sin³ y cos 2y dy from 0 to 𝜋/2.

Question 3

A sales firm receives an average of three calls per hour on its toll-free number. Suppose you were asked to find the probability that it will receive at least three calls, in a given hour:

(a) (i)  which distribution does this scenario fit and why?                           

   (ii) define the variable of interest, X.                                                       

   (iii) what are the possible values of X?                                                     

(b)     What is the probability that in a given hour it will receive at least three calls?

Question 2

The probability that a house in an urban area will be burglarized is 5%. A sample of 50 houses is randomly selected to determine the number of houses that were burglarized.

P (pass) = 0.05 q (failure) = 0.95 n = 50

(a)      Define the variable of interest, X.                                                      

(b)      What are the possible values of X?                                                    

(c)      What is the expected number of burglarized houses?                                  

(d)     What is the standard deviation of the number of burglarized houses?                      

(e)      What is the probability that none of the houses in the sample was burglarized?

The probability that a tutor will see 0, 1, 2, 3, or 4 students

x 0 1 2 3 4

P(x) 4/27 1/27 5/9 ? 5/27

(a)      What is the probability that the tutor sees 3 students?                                              

(b)      What is the probability that the number of students the tutor will see is between 1 and 3 inclusive?        

(c)       What is the expected number of students that the tutor will see?

(d)     What is the standard deviation?

Find the area bounded by the y-axis, the line y = 1, and the arc of y = sin x between x = 0 and x = 𝜋/2.