.    A package of Chips Ahoy Cereal is marked “Net Wt. 12 oz.” The actual weight is normally distributed

       with a mean of 12 oz. and a standard deviation of 0.2 oz. In each of the following, provide sketches

      of the normal distribution curve with appropriate labels and formulas used.

a.     What percent of boxes would be expected to weigh more than 11.75 oz.?                          

b.   In a sample of 2,000 packages, how many would be expected to weigh more than 12.3 oz.?                                                                                                                                                  

c.    What is the probability that a random package would weigh between 11.8 and 12.1 oz.?       

25. If the following waves are superposed y1 = A Cos[k x – w t] and y2 = A Cos[k x + w t] where A = 0.2 cm, f = 10 Hz and c = 10 m/s. (a) Sketch the waveform at time t = 0 and t = 1/40 s. (b) What is the distance between the nodes. (c) Determine the kinetic and potential energy contained within the string section between the a node and an antinode. (d) Show that the total energy between the node and antinode is a constant in time. Why is this physically reasonable?

A 10 g bullet is fired with 450 m/s into a 10 kg block that sits at rest on a wooden table 20 cm from the edge of the table. The bullet gets embedded in the block (perfectly inelastic collision). The block, with the embedded bullet, then slides to the edge of the table and drops down with some initial velocity while leaving the edge of the table. The coefficient of kinetic friction between the block and the surface of the table is k = 0.2. If the table is 1 m high, how far from the point directly below the table’s edge does the block land?

Installing Tesla solar panels in a house costs $18,000. It is expected that the average monthly savings will be 1,000 kWh per month. Assuming that the utility company charges 0.2 per $/kWhr.

1. What is the Present worth of this investment for i=6% and N=15 years?
2. A different approach could be to install energy efficient windows and enhance the insulation for $12,000, which would yield average monthly savings of 700 kWh per month. Assuming the same interest rate and time span. What is the present worth of this alternative?
3. Which option would you choose? Why?

Suppose S = {p, q, r, s, t, u} and A = {p, q, s, t} and B = {r, s, t, u} are events.

x p q r s t u

p(x) 0.15 0.25 0.2 0.15 0.1

(a) Determine what must be p(s).
(b) Find p(A), p(B) and p(A∩B).
(c) Determine whether A and B are independent. Explain.
(d) Arer A and B mutually exclusive? Explain.
(e) Does this table represent a probability istribution of any random variable? Explain.

A person stands at the center of a turntable, holding his arms extended horizontally with a 1.5 kg dumbbell in each hand. He is set rotation about a vertical axis, making one revolution in 2 seconds. Find the new angular velocity if he pulls the dumbbells in to his middle. His moment of inertia (without dumbbells) is 3 kgm2 when his arms are out stretched, dropping to 2.2 kgm2 when his hands are at his middle. The dumbbells are 1 m from the axis initially and 0.2 m from it when moved to his middle.

An enzymatic reaction takes place in a 10 ml solution that has a total citrate (plus citric acid) concentration of 120 mM and an initial pH of 7.00. During the reaction 0.2 millimoles of H+ are produced. The relevant pKa of citric acid is 6.40. A) Calculate the final pH of the solution. B) What would the final pH of the solution be if the citrate were absent from the solution and no other buffering agents were present (assuming a starting pH of 7.00 again, basically, what would be the pH is you added the same amount of acid to that amount of water)?

An investment bank has been asked to underwrite an issue of 10 million shares by a company.

The bank is trying to decide between a best-efforts deal where it charges a fee of $0.2 for each share sold and a firm-commitment deal where it buys the shares for $10 per share.

For the latter deal, the bank considers that the selling price per share is either $10.8 or $9.8.

What are the break-even probabilities of the two selling prices so that the bank is indifferent to the two deals (Assume that all 10 million shares are sold out)?

Question 01: Al Marai offers the customer who buys a 1 kg bottle of milk two free gifts, chosen from the following a chocolate bar, a small bottle of milk, a glass cup, if you purchased milk, what is the probability you randomly select a chocolate bar and a glass cup in that order?

a. 0.00

b. 1.00

c.0.05

d. 0.2

.

Question 02: A box of 24 types of chocolate bars that are made in UAE. Three bars are to be chosen randomly for testing.

how many different combinations of three bars could be selected

A stock's returns have the following distribution:

Calculate the stock's expected return. Round your answer to two decimal places.

Calculate the stock's standard deviation. Do not round intermediate calculations. Round your answer to two decimal places.

Calculate the stock's coefficient of variation. Round your answer to two decimal places.