Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition. It can be used to perform daily tasks such as making to-do lists, reporting the news and weather, and interacting with other smart devices in the home. In 2018, the Amazon Alexa app was downloaded some 2,800 times per day from the Google Play store.† Assume that the number of downloads per day of the Amazon Alexa app is normally distributed with a mean of 2,800 and standard deviation of 860.

(a)

What is the probability there are 2,100 or fewer downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(b)

What is the probability there are between 1,600 and 2,600 downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(c)

What is the probability there are more than 2,900 downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(d)

Suppose that Google has designed its servers so there is probability 0.03 that the number of Amazon Alexa app downloads in a day exceeds the servers' capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google's servers designed to handle? (Round your answer to the nearest integer.)

downloads per day

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.8.

(a) Use the Normal approximation to find the probability that Jodi scores 76% or lower on a 100-question test. (Round your answer to four decimal places.)
1

(b) If the test contains 250 questions, what is the probability that Jodi will score 76% or lower? (Use the normal approximation. Round your answer to four decimal places.)
2

(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?
3 questions

(d) Laura is a weaker student for whom p = 0.75. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?

4

Yes, the smaller p for Laura has no effect on the relationship between the number of questions and the standard deviation. No, the smaller p for Laura alters the relationship between the number of questions and the standard deviation.    

A class has 10 mathematics majors, 6 computer science majors, and 4 statistics majors. Two of these students are randomly selected to make a presentation. Let X be the number of mathematics majors and let Y be the number of computer science majors chosen.

(a) Determine the joint probability mass function p ( x , y ). This generalizes the hypergeometric distribution studied in Sect. 2.​6 . Give the joint probability table showing all nine values, of which three should be 0.

(b) Determine the marginal probability mass functions by summing numerically. How could these be obtained directly? [ Hint : What type of rv is X ? Y ?]

(c) Determine the conditional probability mass function of Y given X = x for x = 0, 1, 2. Compare with the h ( y ; 2 − x , 6, 10) distribution. Intuitively, why should this work?

(d) Are X and Y independent? Explain.

(e) Determine E ( Y ∣ X = x ), x = 0, 1, 2. Do this numerically and then compare with the use of the formula for the hypergeometric mean, using the hypergeometric distribution given in part (c). (f) Determine Var( Y ∣ X = x ), x = 0, 1, 2. Do this numerically and then compare with the use of the formula for the hypergeometric variance, using the hypergeometric distribution

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.83.

(a) Use the Normal approximation to find the probability that Jodi scores 79% or lower on a 100-question test. (Round your answer to four decimal places.)


(b) If the test contains 250 questions, what is the probability that Jodi will score 79% or lower? (Use the normal approximation. Round your answer to four decimal places.)


(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?
questions

(d) Laura is a weaker student for whom p = 0.78. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?

Yes, the smaller p for Laura has no effect on the relationship between the number of questions and the standard deviation.

No, the smaller p for Laura alters the relationship between the number of questions and the standard deviation.    

2.) Suppose that the number of requests for assistance received by a towing service is a Poisson process with rate a = 6 per hour.

a.) Find the expected value and variance of the number of requests in 30 minutes. Then compute the probability that there is at most one request in 30 minute interval.

b.) What is the probability that more than 20 minutes elapse between two successive requests? Clearly state the random variable of interest using the context of the problem and what probability distribution it follows.

3.) Certain ammeters are produced under the specification that its gauge readings are normally distributed with main 1 amp and variance 0.04 amp^2, respectively.

a.) What is the probability that a gauge reading from the test is more than 1.15 amp?

b.) Find the value of a gauge reading of an ammeter such that 20% of ammeters would have higher readings than that. In other words, find the 80-th percentile of gauge readings.

4. ) Suppose that a quality control engineer believes that the manufacturing process is flawed and wishes to estimate the true mean gauge reading. The engineer samples 130 of these ammeters and measures their gauge readings. From these, the engineer obtains the mean and standard deviation of 1.1 amp and 0.18 amp, respectively. Calculate and interpret a 98% confidence interval for the true mean gauge reading.

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.82.

(a) Use the Normal approximation to find the probability that Jodi scores 77% or lower on a 100-question test. (Round your answer to four decimal places.)


(b) If the test contains 250 questions, what is the probability that Jodi will score 77% or lower? (Use the normal approximation. Round your answer to four decimal places.)


(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?
questions

(d) Laura is a weaker student for whom p = 0.77. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?

Yes, the smaller p for Laura has no effect on the relationship between the number of questions and the standard deviation.No, the smaller p for Laura alters the relationship between the number of questions and the standard deviation

1. The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the production cost distribution is normal. Suppose that 46 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. For a single randomly selected movie, find the probability that this movie's production cost is between 51 and 56 million dollars.
4. For the group of 46 movies, find the probability that the average production cost is between 51 and 56 million dollars.

2. Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1.1 month. 18 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )  
2. What is the distribution of x¯? x¯ ~ N( , )
3. What is the probability that one randomly selected person learned to walk when the person was between 10 and 12.5 months old?
4. For the 18 people, find the probability that the average age that they learned to walk is between 10 and 12.5 months old.
5. For part d), is the assumption that the distribution is normal necessary? Yes or No
6. Find the IQR for the average first time walking age for groups of 18 people.
   Q1 = ______ months
   Q3 = ______ months
   IQR: ______ months

3. The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 12. Suppose that 8 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 78.2 and 84.2.
4. For the 8 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 78.2 and 84.2.

4. The lengths of adult males' hands are normally distributed with mean 188 mm and standard deviation is 7.2 mm. Suppose that 17 individuals are randomly chosen. Round all answers to 4 decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 17, find the probability that the average hand length is more than 187.
3. Find the third quartile for the average adult male hand length for this sample size.

5. Suppose that the average number of Facebook friends users have is normally distributed with a mean of 125 and a standard deviation of about 55. Assume fourteen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 14, find the probability that the average number of friends is less than 107.
3. Find the first quartile for the average number of Facebook friends

6. The amount of syrup that people put on their pancakes is normally distributed with mean 57 mL and standard deviation 9 mL. Suppose that 41 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a single randomly selected individual is observed, find the probability that this person consumes is between 57.7 mL and 59.2 mL.
4. For the group of 41 pancake eaters, find the probability that the average amount of syrup is between 57.7 mL and 59.2 mL

A machine shop owner wants to decide whether to purchase a new drill press, new lathe, or new grinder. As shown in the following table, the profit from each purchase will vary depending on whether or not the owner wins a government contract, with the owner estimating a probability of .60 of winning the contract:

Before deciding which item to purchase, the owner needs to decide whether or not to hire a military consultant to assess whether the shop will get the government contract. The track record of the military consultant in predicting whether companies would win government contracts is as follows: For 90% of the companies that won contracts, the consultant had predicted they would win, and for 70% of the companies that lost contracts, the consultant had predicted they would lose. [adapted from Taylor (2004)]

(a) Assuming the consultant would not charge for his assessment, determine the optimal strategy based on the expected value criterion, and state its expected value. (Draw then solve the Decision Tree below)

(b) Determine EVSI (with the consultant regarded as the sample information).

(c) If the consultant were to charge $5,000 for his assessment, what would be the optimal strategy and its expected value?

Can anyone explain all the answer?

1. Horizontal force needed to keep a sled moving along dry (it means not wet) horizontal surface is 10 N. You increase this force up to 20 N. Neglect air resistance.  What can you say about character of motion of a sled now?

a. Sled will continue to move with the same speed.

b. Sled will accelerate for a while up to higher speed and then move with constant, higher speed.

c. Sled will accelerate indefinitely.

d. Sled will move with constant speed two times greater than initial.

2. You try to move a refrigerator of weight 2000 N applying force of 500 N. Refrigerator does not move. The force of friction acting of refrigerator is:

a. 2000 N

b. More than 500 N but less than 2000 N

c. Slightly less than 500 N

d. 500 N

e. Zero.

3. A person rides an elevator standing of a bathroom scale (people are doing strange things). Elevator moves up with constant velocity. What will be the reading of a bathroom scale?

a. more than mg

b. mg

c. less than mg

d. zero

4. Some force acts on an object sitting on the horizontal surface and it accelerates. We increase force twice and perform experiment again. If surface is frictionless, the acceleration of an object will increase:

a. Less than two times

b. Exactly twice

c. More than twice

d. Stays the same.

5. An object is sitting at rest on a horizontal table. Which one of Newton’s laws predicts that normal force acting on this object is equal in magnitude and opposite in direction to the force of gravity (weight) acting on this object?

a. First

b. Second

c. Third

d. Law of gravitation.

A 4 cylinder 4 stroke 2.3 L diesel engine with bore = 12.4 cm and stroke =11 cm. the crank radius is 6.2 cm and with a connecting rod length 15 cm. the compression ratio of the engine is 20 and the combustion efficiency is 97.3 %. If the average speed of the car over the running life of the engine is 56 km/h and the total traveled distance of the engine is 250000 km. note: use the engine speed as 2300 rpm whenever needed, mechanical efficiency is 73 %, indicated work produced from each cycle each cylinder is 1400J, and assume that the injection started 10 degrees bTDC and ends at 25 crank angle degree aTDC.

Determine:

1. The volume of the BDC.
2. The amount of the fuel that didn’t burned in the combustion chamber .
3. The rate of the air flow to the engine if the volumetric efficiency is 70 %.
4. The number of the exhaust strokes that have been happened during the engine life in one cylinder.
5. Indicated mean effective pressure.
6. The torque produced from the engine.
7. The time duration for the injection process.
8. The position of the piston at the end of the injection period.
9. The volume of the combustion chamber at the moment of the injection process.
10. If the mass floe rate of the fuel used if A/F is 19.3 kgair/kgfuel.
11. The specific power of the engine.
12. Based on the dimensions of the bore and the stroke, is this engine square engine or over or under square one?