Reference no: EM13297499
1-A continuous random variable X has a uniform distribution over the interval (-k, 3k), where k is some number. The height of the PDF over this interval is .05. For all other values of X, the PDF=0.
a.) What is the value of k?
b.) What is the probability that X=7.5?
c.) What is the probability that a randomly selected X lies between -10 and 10?
2-Suppose a selective university only considers accepting students with a cumulative grade point average of 3.16 or higher. Students below this threshold are not considered. Suppose the population of students applying to this university has a GPA that is normally distributed with a mean of 3.0 and standard deviation .4.
a) What is the probability that a randomly selected student will meet the GPA threshold?
b) If 50 applicants are chosen at random, what is the probability that 17 or more of them will meet the GPA threshold? (Note: You’ll want to use your answer from part a. If you’re not sure about this answer (and even if you are), be very clear about your calculations for part b.)
3-Suppose 76 stock market mutual funds are chosen at random and their results for the most recent year are recorded. Of these, after fees and expenses, 18 of them earned their investors a return higher than the stock market as a whole. (Note for those interested in investing: this is a pretty realistic figure. Most mutual funds fail to overperform the broader market in a year.)
What is the 97% confidence interval for the population proportion of mutual funds that have a return higher than the stock market as a whole?
|
Determine how large must the reactor be
: A CMFR is to be designed to remove contaminant A from water with a steady-state efficiency of 95 percent. The decay reaction is zeroth order, with a rate constant of 0.1M/h. The inlet concentration of A is 0.5 M.
|
|
What is the specific heat ratio
: The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5
|
|
Explain how many grams of sodium formate nacho2
: How many grams of sodium formate, NaCHO2, would have to be dissolved in 1.3 L of 0.45 M formic acid (pKa 3.74) to make the solution a buffer for pH 3.75
|
|
Determine the tension in the cable closer to the painter
: A scaffold of mass 57 kg and length 6.5 m is supported in a horizontal position by a vertical cable at each end. What is the tension in the cable closer to the painter
|
|
What is the probability that a randomly selected student
: If 50 applicants are chosen at random, what is the probability that 17 or more of them will meet the GPA threshold? (Note: You’ll want to use your answer from part a. If you’re not sure about this answer (and even if you are), be very clear about yo..
|
|
What is the total equivalent through volume on the approach
: An intersection approach volume is 1,500 veh/h and includes 12% left turns with a through-vehicle equivalent of 2.3 tvu's/left turn. What is the total equivalent through volume on the approach
|
|
What is the length of the annuity time period
: You are considering an annuity which costs $127,392 today. The annuity pays $7,700 a year at an annual interest rate of 4.5 percent. What is the length of the annuity time period?
|
|
Explain the possible constitutional and stereoisomers
: Draw and name all the possible constitutional and stereoisomers of the monochlorinated products formed by the free-radical chlorination of 2-methylbutane. Count any pair of enantiomers as two different products
|
|
Determine what is the outlet air temperature
: A total of 13,610 kg/h of air at 1 atm abs pressure and 15.6C is to be heated by passing over a bank of tubes in which steam at 100C is condensing. The tubes are 12.7mm OD, 0.61 m long, and arranged in-line in a square pattern with Sp=Sn= 19.05mm.
|