Suppose that the average number of equipment breakdowns at a factory per week is 5. Later we’ll show that the average is our best guess at the expected value of ? = ?ℎ? ?????? ?? ????????? ?????????? ?? ? ????? ???? (assuming that this distribution stays the same across multiple weeks.) It’s also known that, through some other sample statistic, that our best guess at the standard deviation of X given the data is 0.8. a. With the help of our boy Chebyshev, find an interval such that we can be at least 90% that the number of breakdowns next week will fall within that range. b. Suppose that the supervisor promises the board of directors that the number of breakdowns will rarely exceed 8 in a one- week period. Is the supervisor safe in making this claim? Why or why not? c. Google Chebyshev and just stare at this guy’s magnificent beard for a few seconds. You don’t need to write anything down. You’re welcome.

Complete parts​ (a) and​ (b) below.

The number of dogs per household in a small town

(a) Find the​ mean, variance, and standard deviation of the probability distribution.

Find the mean of the probability distribution.

u=___(Round to one decimal place if needed)

Find the variance of the probability distribution.

o2=___(round to one decimal place if needed)

find the standard deviation of the probability distribution

o=____(round to one decimal place when needed)

(b) Interpret the results in the context of the​ real-life situation.

A) a household on average has 0.5 dogs with a standard deviation of 0.9 dogs

B. A household on average has

0.5

dog with a standard deviation of

eleven

dogs.

C. A household on average has

0.9

dog with a standard deviation of

0.5

dog.

D.

A household on average has

0.8

dog with a standard deviation of

0.9

dog.

.9

An ultrasound machine in a hospital uses a sound source at 19.00000MHz.

1. Assuming that the speed of the ultrasound in the body is same as water (1440 m/s), determine the wavelength in the body.
2. If blood cells are moving towards the sound source at a speed of 0.8 m/s, at what frequency do the crests of the sound wave pass through the blood cell?
3. What is the frequency of the sound waves reflected back towards the source by the blood cells?
4. 1. If the sound level intensity is 17.0 dB at a point d₁ = 6.8 cm from the source, what is the sound intensity at that point in W/m². (We can assume that 0 dB is referenced to 10^-12 W/m²).
   2. Assume that sound is emitted from a point source, so that the intensity decreases quadratically with distance. What is the intensity level in dB at a point d₂ = 2.0cm from the source?

A certain soccer player has made 80% of her penalty shots over her professional career. She is injured, but recovers. On her return, she only makes 5 of her first 10 penalty shots.

1. Assuming she is actually just as good at penalty shots as she was before her injury and each shot is independent of each other shot, calculate the probability of her making exactly 5 out of 10 penalty shots.

2. Calculate the probability of her making 5 or fewer penalty shots out of 10, assuming she is still an 80% shooter.

3. The previously calculated value could be thought of as the p-value for a hypothesis test. The null hypothesis for this test is H₀: p=0.8. Define p in context and write the alternative hypothesis for this test.

4. What conclusion would you draw about the soccer player’s penalty shot ratio?

Assume an economy where there are no supply constraints and where businesses want to invest 15 billion; government collects 20 billion in income taxes and also spends 20 billion; next exports are -5 billion; autonomous consumption is 10 billion; and the MPC is 0.8

a) Write out the Aggregate Expenditure function and calculate the equilibrium level of income.

b Now assume that the government increases both taxes and expenditures by 25 percent. What happens to the equilibrium level of income?

8)A math course has 3 tests during the semester and a test. Each test counts for 20 percent of the course grade, and the test counts for 40 percent of the course grade. JJ has scored 50 out of 100 in each of the 3 tests. What grade does JJ need to get in the test (score out of 100) in order to reach the score of 60 for the whole course?

1. In China, the fertility rate is 1.8 children per woman in childbearing age. What does this mean for the population growth in the long run and why?

2. In Country B the sex ratio at birth is 0.96. How does this compare to the normal sex ratio and what does this mean for country B?

3. The share of people aged 15-64 in China was 73% in 2010 and is projected to fall to 65% in the next few years. Western companies that have been building factories in China for past few decades are now gradually looking to relocate to other places in Asia, such as Cambodia and Bangladesh. What could be the link between the two phenomena?

4. In Japan, life expectancy is 84 years, the share of the population aged 65 and above is 28%, and the economic growth is 0.8% per year. How are these three statistics connected?

Typical ultrasound consists of about 25 images extracted from a full-motion ultrasound examination. Each of these images consists of 512 by 512 pixels, each with 8 bit intensity information. a) What is the total number of bits in the 25 images?

b) Ideally the doctors would like to playback the ultrasounds at 30 frames per second. Assuming that when playing back each ultrasound frame is compressed by a factor of 0.8, what is the data rate required to play the ultrasound?

c) Consider now that this ultrasound needs to be viewed in real-time at a remote location using wireless communication. If the communication system has a signals to noise ration of 30dB and an overhead of 15%, what is the minimum bandwidth required for this communication.

d) Assume a practical error correction method is able to achieve a 75% of the above data rate. How many signal levels are required to achieve this data rate?

1. A gas mixture containing a solute with a concentration of Y₁=0.02 to be absorbed in a packed tower. The gas-liquid equilibrium is described by: Y^*=1.0X.

(a) (10%) To achieve a 99% solute recovery, calculate the required gas phase overall mass transfer unit N_tOG and the composition X₁ at the liquid exit. X₂=0.0001 at the liquid inlet with L/G=1.2.

(b) (10%) For pure liquid inlet with L/G=0.8, what is the maximum percentage solute recovery?

2. For a packed tower for gas absorption operation, under a given operating condition, it is found that kya=kxa=0.026 kmol/m2.s. The equilibrium equation is given by: y=5x. Given that ky?G0.8, calculate the percentage reduction in overall mass transfer coefficient if the gas flow rate is doubled while the liquid flow rate remains unchanged.