2. Consider a gas station's daily sales. Let Y be the volume of gas sold per day in 1000s of gallons. Assume the distribution of Y follows this pdf: 1sxs2 S (v)=. else a. What value of k is required for the above function to be a valid pdf? b. Verify that the function given is a valid probability density function c. Determine the cumulative distribution function (cdf) of the random variable d. Compute the probability that there is exactly 1500 gallons of sales on a given day (Hint: FindP(r - 1.5) )

A spinner contains the values 0 up to, but not including, 1. The outcomes of the spinner are equally likely, so the density curve is described by a uniform distribution as shown. Let X = the random number spun on the spinner. Height = 1 0 Random number What is the mean of X and the median of X? Mean = 0.25 Median = 0.5 Mean = 0.5 Median = : 0.5 Mean 0.75 Median 0.5 Mean = 0.5 Median = 0.25 Mean = 0.5 Median = 0.75 = -

A Normal distribution A.All of these are correct. B.can be completely specified by a mean and a standard deviation. C.has an area of exactly 1 underneath the density curve. D.is symmetric.

Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let  denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.   a.  Select the probability density function.   1.     2.     3.     4.         b.  What is the probability of generating a random number between 0.15  and 0.85 (to 1 decimal place)?   c.  What is the probability of generating a random number with a value less than or equal to 0.3  (to 1 decimal place)?   d.  What is the probability of generating a random number with a value greater than 0.6  (to 1 decimal place)?   e. Using 50  random numbers given below, compute the mean and standard deviation.   0.467202 0.370629 0.966103 0.003795 0.877402 0.626396 0.816661 0.955063 0.569638 0.793645 0.641853 0.189704 0.519289 0.876775 0.016900 0.232961 0.807478…

A probability density curve is described by 2 line segments. The first connects (0, 1/7) and (3.5. 1/7), and the other connects (3.5, 1/7) to the x-axis. Part A: Sketch the probability density curve as described. (Be sure to label all values) Part B: Determine the x-value where the second segment crosses the x-axis. Part C: Determine P(X 0.05). Part E: Determine the median x-value of this distribution.

Do you dislike waiting in line? Supermarket chain Kroger has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 stores. Using a new system called QueVision, which allows Kroger to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 26 seconds (InformationWeek website). Assume that waiting times at Kroger are exponentially distributed. a. Which of the probability density functions of waiting time is applicable at Kroger? 1 а. f(x) — er = for æ >0 e 26 1 b. f(x) = 1 e 26 26 for æ >0 e 1 c. f(x) = 1 for æ 0 26 Select your answer - v b. What is the probability that a customer will have to wait between 15 and 30 seconds (to 4 decimals)? c. What is the probability that a customer will have to wait more than 2 minutes (to 4 decimals)?

Assume that the machine yields the item selected 90 percent of the time, and returns nothing 10 percent of the time. Three individuals attempt to use the machine. Let X be defined as the number of individuals who obtain the item selected. How many different values are possible for the random variable X? Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order.

C Arandom variable is normally distributed with a mean of μ-50 and a standard deviation ofto=5 a. Which of the following graphs accurately represents the probability density function? A B 40 50 55 σ=5 60 d=5

3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.