Reference no: EM131385965

Problem 1: Lifetime of a VLSI chips manufactured by company X is a normal distribution with μ = 5 * 10⁶ hours and σ = 5 * 10⁵ hours. Your company needs a batch that has at least 95% of the chips with life time greater than 4* 106 hours.

Will you close this deal?

Problem 2: A battery manufacturer claims its product is normally distributed with a life time of average 3 years and a standard deviation of 0.5 years. What is the probability that a battery you purchased lasts more than 2 years?

Problem 3.

a. Fibonacci sequence is found everywhere in nature. Do a google search and read about the presence of 'golden ratio' and the sequence in engineering designs. Write about one example that interests you.

b. Write a Matlab code to generate the Fibonacci sequence to generate the first 20 terms.

c. Plot the golden ratio for the sequence and notice how the ratio approaches a constant.

Problem 4. Write a code to carry out 100 iterations on the recurrence relation

X_n+1 = 4X_n(1 - X_n)

i. Given initial condition X(0) = 0.2
ii. Given initial condition X(0) = 0.2001
iii. List the final 10 iterations in each case.