The foreman of a bottling plant has observed that the amount of soda in each 32-ounce bottle is actually a normal distributed random variable, with a mean of 32.2 ounces and a standard deviation of 0.3 ounce. A customer buys a carton of four bottles.

A. What is the probability that the mean amount of the four bottles will be greater than 31.9 ounces?

B. What is the probability that the mean amount of the four bottles will be between 31.8 and 32.4 ounces?

C. Below what amount does 55.57% of the mean amount fall?

Consider the following multiple regression equation relating a machinist's performance rating on a new machine (RATING) to the following three independent variables.

WKEX - number of years work experience as a machinist

TSCORE - mechanical aptitude score

Years - age

^Rating = 12.5 + 0.8 WKEX + 0.32 TSCORE + 0.3 YEARS

a) Explain all of the steps for finding the value of R^2 (coefficient of determination) which are associated with finding the variance inflation factor (VIF) associated with the independent variable YEARS.

An air bottle used for scuba diving breathing apparatus has a volume of 30 l. After it has been used, the pressure and temperature of the remaining air in the bottle are 0.3 MPa and 24 ◦C. Before the apparatus is used again, it is charged with air at temperature of 50 ◦C until the pressure in the bottle reaches 6 MPa. The charging processes is fast, and can be assumed to be adiabatic.

Questions: (a) Calculate the mass of air to be added to the bottle.

(b) What is the temperature of the air in the bottle at the end of the charging process?

The Chahad Bank wants to open a new branch in a distant city with very different economic conditions. Currently, the bank has an expected return of 15% with a standard deviation of 7%. The new branch is expected to have a return of 20% with a standard deviation of 10%. The correlation between the bank's returns and the returns from the new branch is -0.3. The new branch is expected to contribute 10% of the bank's revenues. What is the expected return for the bank if they add the new branch?

please show work

a. You are studying an economy with an income tax rate, ti, of 32% and an MPS of 0.3. It is currently suffering from a “recessionary gap” of $500 m. (i.e., Eqm Y Y full employment, FE, aka Yn). Make the necessary calculations for the to policy that it should institute; who does what? Provide the full name of this policy.

b. Compare this economy to one without income taxes to explain the term “automatic stabilizer.” [Hint: Let I change and compare the I multipliers in each of these economies.]

The bearing capacity, ?, of soil under a square foundation of size 9 ft^2 is determined to be a random variable with a mean of 3 ksf and a standard deviation of 0.3 ksf. The applied axial load, ?, acting on the foundation is also a random variable with a mean of 16 kip and a standard deviation of 2 kip. Assume ? and ? are statistically independent normal variables. Using the limit state function of the form ?() = 9?– ?, use the normal format approach to calculate the reliability index and the corresponding probability of failure of the foundation.

In a sample of 75 steel wires, the average breaking strength is 50 kN, with a standard deviation of 1.9 kN. a) Find a 99% confidence interval for the mean breaking strength of this type of wire. b) An engineer claims that the mean breaking strength is between 49.7 kN and 50.3 kN With what level of confidence can this statement be made? c) How many wires must be sampled so that a 99% confidence interval specifies the mean breaking strength to within 0.3 kN?

Calculate the following probabilities using the standard normal distribution. (Round your answers to four decimal places.) (a) P(0.0 ≤ Z ≤ 1.8) (b) P(−0.1 ≤ Z ≤ 0.0) (c) P(0.0 ≤ Z ≤ 1.46) (d) P(0.3 ≤ Z ≤ 1.58) (e) P(−2.02 ≤ Z ≤ −1.72) (f) P(−0.02 ≤ Z ≤ 3.51) (g) P(Z ≥ 2.10) (h) P(Z ≤ 1.63) (i) P(Z ≥ 6) (j) P(Z ≥ −9)

A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of cheese. The estimate must be within 0.3 milligram of the population mean. Assume the population standard deviation is 2.9 milligrams. Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Determine the minimum sample size required to construct a 98% confidence interval for the population mean. Which level of confidence requires a larger sample size? 90% 98%

Researchers have been studying the association between cigarette smoking and caffeine intake and

Parkinson's Disease for more than 40 years. The results of a study by Checkoway et al. (2002) follow:

Ever having smoked cigarettes resulted with an odds ratio (OR) = 0.5 (95% confidence interval (CI):

0.4, 0.8).

The OR for current smokers was OR = 0.3 (95% CI: 0.1, 0.7).

Among ex-smokers the OR = 0.6 (95% CI: 0.4, 0.9).

Interpret the three ORs (in your own words).