A game is played with two sensible 6-sided dice. The player rolls the dice.
If the measure of the dice is 7 or less, the player loses $3.
If the measure of the dice is 8, 9, or 10, the player procures back the first speculation.
If the measure of the dice is at least 11 conspicuous, the player wins $15.
The discretionary variable X is a player's advantage (in $) from playing this game.
a) Find P(X = 0). Offer your reaction as a part in least terms.
P(X = 0) = Blank 1. Fill free, read including content.
b) Find E(X). Offer your last reaction as a decimal. If changing, accommodate 2 decimal spots.
E(X) = Blank 2. Fill free, read including content. dollars
c) Find the standard deviation s for the sporadic variable X.
Offer the last reaction as a decimal acclimated to 2 decimal spots.
s = Blank 3. Fill free, read incorporating content. dollars
A test was given to a get-together of understudies. The assessments and sexual direction are summarized underneath
A B C Total
Male 13 18 10 41
Female 17 16 5 38
All out 30 34 15 79
If one understudy is picked capriciously from the people who ventured through the assessment,
Find the probability that the understudy got 'A' GIVEN they are male.
A machine allots juice into bottles and the fill levels are regularly scattered with a mean of 1000 milliliters and a standard deviation of 15 milliliters.
Using the normalcdf request on your little PC, find the going with probabilities precisely to 4 decimal spots.
a) Find the probability that a container is filled between 995 ml and 1010 ml.
The probability is Blank 1. Fill free, read incorporating content.
b) Find the probability that a compartment is stacked up with under 1020 ml.
~19~
The probability is Blank 2. Fill free, read including content.
An assessment is done In Sydney to survey the degree of people living there who have gone outside of Australia. Past research has found that this degree is comparable to by and large 28%.
a. Find the base model size needed for the examination to get in any event 5% squirm room in an unpleasant 95% sureness Interval for this degree (use k=1.96)
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3. a. Provide mathematical definitions and units of work, K.E., P.E. b. Provide a mathematical definition of torque, and provide its unit in the MKS system of units. c. As is customary, physicists deal mostly with forces and energy. An im- portant part of their studies is to find the speed of objects under various cir- cumstances. Therefore, one of these guys dropped a heavy stone from a height of 35 m. The physicist wants to know how fast this object will be going just before hitting the ground if we are to ignore frictional forces. d. A large segment of the US population visits recreational parks (Kings Do- minion, Busch Gardens, etc.) with their children. In these parks, children are usually thrilled by their rides on a roller coaster. A typical and simple situation is described here. A roller coaster is pushed to the top of a struc- ture by mechanical forces. To be more specific, a roller coaster weighing 768 lb starts from rest at point A in the figure below and begins to coast down the track. If the friction force along the tracks is 1 1.0 lb, how fast will the roller coaster be going at point B? and then at point C?I. On the space provided, write DR if the conclusion is reached thru deductive reasoning; and write IR if the conclusion is reached thru inductive reasoning: 1. A square has four equal sides. Our window has four equal sides. Therefore, our window is a square.. 2. If X = Y and Y = Z, then X = Z. 3. My Geometry teacher this semester is skinny. My Geometry teacher last semester was skinny. Therefore, Geometry teachers are skinny. 4. All prime numbers are not divisible by any number except 1 and itself. 11 is divisible only by 1 and itself, Therefore, 11 is a prime number. 5. Angles A, B and C are angles inside a triangle. The sum of the angles of any triangle equals 180'. Therefore, the sum of angles A, B and C equals 180'. 6. Acute angles are less than 90' and angle @ is 42', so this angle @ is acute. 7. All numbers ending in 0 or 5 are divisible by 5. 80 ends with 0 and 45 ends in 5. Therefore, 80 and 45 are divisible by 5. 8. Sets A and B are equal Equal sets are equivalent Therefore, sets A and B are equivalent. 9. Mass and weight are directly proportional Mass is directly proportional to force. Therefore, weight is directly proportional to force. 10. The symbol x and * indicate multiplication operation. The symbol / and + indicate division operation. Therefore, x," , / and +are operation symbols. II. PROBLEM SOLVING Problem #1. Four siblings, namely : Ammie, Jenn, Chard and Sonny watch their Dad's basketball game. Like others, they are sometimes childish and there are moments of tantrums. Consider the following to guess their seating arrangement: A. Ammie does not like to sit near Chard. B. The boys want to sit together. C. Jenn doesn't like to sit near Chard either. D. Sonny is sitting between a boy and girl. E. Ammie is sitting on the seat at the far left of the group. Seat No. 1 Seat No. 2 Seat No. 3 Seat No. 4Problem 1. You have collected data from travel surveys about the number of recreational trips a household takes in a month: A. Perform a linear regression on the number of recreational trips made, write out the equation and provide explanation on the notations used in the equation. B. On average, how many trips would you expect a household of four members to make in a given month, assuming two of them are children under 12, one of them is a worker, and their annual income is $56,000? C. What is the effect on the number of recreational trips if the household size is increased by one? If the answer to the question is "it depends," say what it depends on, and explain how your answer might differ for the different possibilities. D. Your supervisors are curious about the role household size and composition plays in recreational trip making. However, they haven't taken any courses in statistics or engineering (that's why they hired you as a specialist!). Answer their question without using any technical or mathematical language. Household Size Children under 12 Workers Income Recreational trips 1 1 0 0 7000 0.9 2 2 18000 0.7 49000 0.5 4 0 32000 0.6 36000 1.3 30000 0.1 59000 0.5 38000 0.2 SW AND W W N A NU NU 34000 2 47000 1.6 34000 1.4 27000 0.6 28000 0.7 55000 1.7 15 23000 0.4a. Provide mathematical denitions of K..,E P.E. and give their units in the MKS system of units. b. What is conservation of energy? 0. A large segment of the US population Visits recreational parks (Kings Do- minion, Busch Gardens, etc.) with their children. In these parks, children are usually thrilled by their rides on a roller coaster. A typical and simple situation is described here. A roller coaster is pushed A ~ to the top of a structure by mechanical forces. To be more specic, a roller coaster weighing 58.8 N starts from rest at point A in the figure below and be- gins to coast down the track. If the friction force along the tracks is 4.0 N, how fast will the roller coaster be going at point B? and then at point C? lm
