Question Suppose it is known that 5% of the eggs (i.e., a fraction of 0.05) supplied by a supermarket are broken. I buy a carton of 24 eggs. Answer the following questions: (3 + 2+ 3+ 2 pts) (a) What is the probability that two or more eggs are broken in the carton? (Show Excel formula used, as well as the final numerical answer in decimals) (b) How many broken eggs do you expect to see in the carton on an average? (answer may or may not be a whole number) (c) What is the usual range of the number of broken eggs in the carton? (provide two numbers for the range) (d) Would having 3 broken eggs in the carton be unusual? (Provide a 1-2 sentence justification for your answer, otherwise no credit)

An elevator in an apartment building has a load restriction of 12 people or 2000 pounds. The weights of the residents of the apartment building are normally distributed with mean μ = 153.3 pounds and standard deviation σ = 49.8 pounds. If 12 residents are on the elevator at any given time, what is the probability the total weight of the group will exceed the load restriction?

 A police officer found that the distribution of cars speeds in a highway is normal with the average speed of 90 kmph and the standard deviation of 6 kmph.   Find the percentage of drivers who drive in that highway with a speed more than 108 kmph. What percent of cars have a speed above 102 kmph? If the minimum allowed speed is 70 kmph and the maximum is 105 kmph, What is the percentage of drivers who must receive a driving ticket due to inappropriate speed?

Ken is 63 years old and unmarried. He retired at age 55 when he sold his business, Understock.com. Though Ken is retired, he is still very active. Ken reported the following financial information this year. Assume Ken files as a single taxpayer. Ken won $1,680 in an illegal game of poker (the game was played in Utah, where gambling is illegal). Ken sold 1,480 shares of stock for $32 a share. He inherited the stock two years ago. His tax basis (or investment) in the stock was $31 per share. Ken received $29,800 from an annuity he purchased eight years ago. He purchased the annuity, to be paid annually for 20 years, for $250,320. Ken received $14,200 in disability benefits for the year. He purchased the disability insurance policy last year. Ken decided to go back to school to learn about European history. He received a $980 cash scholarship to attend. He used $540 to pay for his books and tuition, and he applied the rest toward his new car payment. Ken’s son, Mike, instructed his employer to make half of his final paycheck of the year payable to Ken as a gift from Mike to Ken. Ken received the check on December 30 in the amount of $1,820. Ken received a $850 refund of the $4,080 in state income taxes his employer withheld from his pay last year. Ken claimed $12,930 in itemized deductions last year (the standard deduction for a single filer was $12,400). Ken received $34,800 of interest from corporate bonds and money market accounts. 2. Complete page 1 of Form 1040 through line 9 and Schedule 1 for Ken.

3. Let Vi, V2, V3, V4, and Vs be vectors in R'. Consider the following conditii (i) {V1, V2, Va) is linearly independent (ii) {v2, V, Vs) is linearly independent. (iii) {V1, V2, Va} is linearly dependent. (iv) {V1, V3, Vs) is linearly dependent. (v) {V2, V3, Vs) is linearly dependent. For each of the following, determine which of the above conditions hold true for the configuration of vectors shown. You do not need to justify your answer. V3A V4 Vi (b) VA V4 Vix (c)

Sam is trying to move a dresser of mass m and dimensions of length L and height H by pushing it with a horizontal force F applied at a height h above the floor. (Figure 1)The coefficient of kinetic friction between the dresser and the floor is plk and g is the magnitude of the acceleration due to gravity. The ground exerts upward normal forces of magnitudes Np and No at the two ends of the dresser. Note that this problem is two dimensional. Figure 1 of 1 L m F H h Р INE ÑO Part A If the dresser is sliding with constant velocity, find F, the magnitude of the force that Sam applies. Express the force in terms of m, g, and jk. Part B Find the magnitude of the normal force Np. Assume that the legs are separated by a distance L, as shown in the figure. Express this normal force in terms of m, 9, L, h, and pk. Part C Find the magnitude of the normal force No. Assume that the legs are separated by a distance L, as shown in the figure. Answer in terms of m, g, Mk, h, and L. Part D Find hmnx, the maximum height at which Sam can push the dresser without causing it to topple over. Express your answer for the maximum height in terms L and plk.

3. 3. (30 points) Gears and Angle of Twist c = 30 mm TOON. D - 120 mm 500 mm 700 mm A simple 2 shaft gear system is shown below. Shaft AB is fixed to a wall at A. Each shalt is made of steel with a maximum allowable shear stress Tmax <60 MPa and G77.2 GPa Determine the following a. Torque in shaft AB (TAB) b. Using Tmax is 60 MPa, determine the required diameter of shaft AB c. D (angle of twist at D) cannot exceed 1" (=pi/180 radians), determine the required shaft diameter of shaft AB and CD it they must be the same diameter