In a group consisting of NT =500 marbles, the mean weight and s.d. value of a marble are 5.02 g and 0.3 g, respectively. 100 marbles are randomly being taken from this group of marbles. Calculate the expected ratios of sample marbles whose total weight a) varies between 4.96-5.00 g, b) is more than 5.10 g

North Shore Inc. is considering two projects with the following probability of outcome and cash flows.

State of economy        Probability of outcome                Cash flows ($)

                                                                                       A                     B

Strong                                    0.2                                   700                550

Normal                                   0.5                                   400                400

Weak                                      0.3                                    200                300

Compute the expected net present value, standard deviation, and coefficient of variation of each of the project.

A call centre manager in an insurance company is interested in knowing the pattern of calls for cancellation. The number of cancellation calls an agent receives per hour follows a Poisson distribution with a mean of 1.2.

What is the probability that an agent receives more than two cancellation calls for the next three hours?

a)0.3 b)0.823 c)0.7 d)0.177

The MB Company is considering investment in one of the following mutually exclusive projects.Cash inflows of foreseeable next four years are given below (cash inflows 000 dollars)

Probabilty Project K Project L

0.15 4250 4250

0.2 4750 5250

0.3 5250 6250

0.2 5750 7250

0.15 6250 8250

Suppose a batch of metal shafts produced in a manufacturing company have a variance of 6.25 and a mean diameter of 206 inches.

If 90 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.3 inches? Round your answer to four decimal places.

We have:

                    P(A) = 0.75

                    P(B|A) = 0.9

                    P(B|A′) = 0.8

                    P(C|A ∩ B) = 0.8

                    P(C|A ∩ B′) = 0.6

                    P(C|A′ ∩ B) = 0.7

                    P(C|A′ ∩ B′) = 0.3     

Compute:

              a) ?(?′| ?′)

              b) P (?′ ∪ ?′)

              c) ?(? ∩ ? ∩ ?)

              d) P(C)

              e) ?(? ∩ ? ∩ ?)’

              f) P(B)

              g) P(AUBUC)

1. An air conditioner using R134a as the working fluid operates on an ideal vapour compression system between 0.3 and 0.8 MPa. If the specified capacity for air conditioning is 20 kW. What would be its capacity for food freezing for which the evaporator temperature -20^oC. Show the cycle on a PH diagram and explain the effect of the changes to the compressor and condenser respectively.

How nature of friction and its magnitude varies based on surface characteristics? Also assume that you
are moving a rectangular block of weight 350 N in a rough horizontal plane having a coefficient of friction
0.3. In what way you will find the magnitude of force which can move the block while acting at an angle of
27 degree with horizontal?

The position of a 0.30-kg object attached to a spring is described by

x = (0.22 m) cos(0.3?t)

(a) Find the amplitude of the motion.
m

(b) Find the spring constant.
N/m

(c) Find the position of the object at t = 0.26 s.
m

(d) Find the object's speed at t = 0.26 s.
m/s

Parker Plastic, Inc., manufactures plastic mats to use with rolling office chairs. Its standard cost information for last year follows: Standard Quantity Standard Price (Rate) Standard Unit Cost Direct materials (plastic) 9 sq ft. $ 1.30 per sq. ft. $ 11.70 Direct labor 0.3 hr. $ 13.50 per hr. 4.05 Variable manufacturing overhead (based on direct labor hours) 0.3 hr. $ 1.30 per hr. 0.39 Fixed manufacturing overhead ($619,080 ÷ 938,000 units) 0.66 Parker Plastic had the following actual results for the past year: Number of units produced and sold 1,000,000 Number of square feet of plastic used 12,800,000 Cost of plastic purchased and used $ 15,360,000 Number of labor hours worked 336,000 Direct labor cost $ 4,200,000 Variable overhead cost $ 1,700,000 Fixed overhead cost $ 393,000

Required: Calculate Parker Plastic’s variable overhead rate and efficiency variances and its over- or underapplied variable overhead.