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Que-1. The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs
a. None fuses
b. Not more than 2 fuse
c. More than 2 fuse

Que-2. A supplier of components to an electronic industry makes a sophisticated product which sometimes fails immediately it is used. He controls his manufacturing process so that the proportion of faulty products is supposed to be only 5%. Out of 400 supplies in a batch, 26 prove to be faulty. Verify the manufacturer’s claim. Use 0.05 level of significance.

Que-3. The ages of husbands and wives in a community were found to have a correlation coefficient equal to +0.8; the average of husbands’ ages was 25 years and that of wives’ ages 22 years; their standard deviations were respectively 4 and 5 years. Find the two lines of regression and from the lines ,measure
a. The expected age of husband when wife’s age is 12 years
b. The expected age of wife when husband’s age is 33 years
2. From the data given below calculate the value of first and third quartiles, second and ninth deciles and forty-fifth and fifty-seventh percentiles.

Height in
centimeters Number of
students Cumulative
frequency
161-167 79 79
167-173 92 171
173-179 60 231
179-185 22 253
185-191 5 258
191-197 2 260
Total 260
let f(x)=cosx
xo=0,x1=.6,x2=.9
find linear and quadratic interpolation
You are given a diabetes data set (http://archive.ics.uci.edu/ml/datasets/Pima+Indians+Diabetes). You are required to build a classification model to predict if a test result is positive or negative. (16)
(a) Explain the method you are going to use.
(b) Describe the data set and possible data pre-processing.
(c) Explain the process for classification model building.
(d) Show and explain your model.
(e) Discuss the accuracy of your model.
Solve the following nonlinear BVP using finite difference methods using MAT-
LAB.
yy′′ +(y′)2 +1 = 0, y(1) = 1,y(2) = 2
. Take N=100, accomplish the following:
1 You code should display three columns namely x, approx. Solution and residual.
2 Plot of x vs solution.
Consider the scheme
yn+1 −2yn +yn−1 =h^2 4 (fn+1 +2fn +fn−1)
where fn = f(xn,yn) etc. is used to solve the initial value problem
y′′ = f(x, y), y(x0) = y0, y′(x0) = y0′
(a) Show that the method has the global error of order 2 when applied to IVP
(b) Show that this method is stable for any value of hk when applied to
y′′=−k^2y k>0
A tank was 1/2 full of water.after 420 gaallons had been taken out it was 1/8 full.Find the capacity of the tank.
how many volts solar module do i need to fully charge a 200w/hr battery?
a principle sum of money is loaned to an account paying interest at 11.67% compounded quaterly for 8 years and 6 months,
(1)determine the interest rate i per period
(2) determine the total number of interest period n of this transaction.
Assume that the inquiries are normally distributed with a standard deviation of 300. Would you take up the offer. Show details of your calculations.
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