i) What is the probability that a consumer will need to pay for signit mechanical repairs less than 18 years after the car is purchased? (i.e. less than 8 years after the warranty period expires) nei tasu ii) It can be shown from the above sef equation that the expected time until the consumer would need to pay for significant mechanical repairs is E(T) ≈ 13.86. Use this information to determine the variance Var (I) of the variable T. dibited.
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for part 2) why are the limits on the
- QUESTION 2 Delta Airlines quotes a flight time of 4 hours, 3 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 4 hours and 4 hours, 12 minutes. (a) Show the graph of the probability density function for flight time. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 234, 240, 246, 252. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/12, 1/6, 1/4. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/12 unit long vertical line segment begins at 240 on the horizontal axis. A 1/12 unit long vertical line segment begins at 252 on the horizontal axis. A 12 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/12 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded…The 3 month demand for a spare car part has the following probability mass function: x 0 1 2 p(x) 0.25 0.5 0.25 a) What is the probability that there will be at most 1 unit of demand during the time period? b) What is the variance of the demand?QUESTION 10 Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2. What are the values for a and b? a. 2 and 6 b. Cannot answer with the information given. c. 0 and 4 d. Can be any range of x values whose length (b − a) equals 4. QUESTION 11 The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a ≤ x ≤ b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices. QUESTION 12 Which of the following is true about f(x) when X has a uniform distribution over the interval [a, b]? a. The values of f(x) are different for various values of the random variable X. b. f(x) equals one for each possible value of X. c. f(x) equals one divided by the length of the interval from a to b.…
- QUESTION 14 The function that defines the probability distribution of a continuous random variable is a a. uniform function. b. probability density function. c. normal function. d. either normal of uniform depending on the situation.Question 17 If X is a random variable with the probability density function: f (x) = c|x|, for - 1 < x < 1 and 0 otherwise. What is the value of c? Please round your result to one decimal place. Correct Answer:_______________________Question 1 : Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is f(x) = 3 x 2 (400)3 , 0 ≤ x < 400. (a) Compute the probability the a certain part will fail in less than 200 weeks. (b) Compute the mean lifetime of a part and the standard deviation of the lifetime of a part. (c) To decrease the probability in part (a), four independent parts are placed in parallel. So all must fail, if the system fails. Let Y = max{X1, X2, X3, X4} denote the lifetime of such a system, where Xi denotes the lifetime of the ith component. Show that fY (y) = 12 y 11 (400)12 , y > 0. Hint : First construct FY (y) = P(Y ≤ y), by noticing that {Y ≤ y} = {X1 ≤ y} ∩ {X2 ≤ y} ∩ {X3 ≤ y} ∩ {X4 ≤ y}. (d) Determine P(Y ≤ 200) and compare it to the answer in part (a)
- Question 7 According to the Almanac of Questionable Statistics, Vol 4 (2012), the probability of a mass squirrel uprising in any given year is 0.11 and the probability that cats and dogs will sign a peace treaty allowing them to live together peacefully in any given year is 0.34. If we presume that these two events are independent, what is the probability of both happening next year? Answer in decimal form. Round to 4 decimal places as needed.Question 18 In a small town, the mean and standard deviation of the internet bill per month per household are $30 and $5, respectively. The town has in total 400 households. Using the central limit theorem, what is the probability that the total internet bill of the entire town is no more than $12100 in a month? (Choose the following correctly)Question 4 (Part B a-c)A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order. The Petrol station is considering adding a second pump with an attendant to service customers. The station would pay that person the same $10 per hour. What is the probability that no customers are in the system (Po)?b. What is the average number of customers waiting for service (Lq)?c. What is the average number of customers in the system (L)? SHOW ALL WORKINGS
- Question 1 In a study conducted for the state Department of Education, 30 percent of the teachers who left teaching did so because they were laid off. Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that exactly 3 of them were laid off. .0090 .2001 .2668 .3000 Question 2 The chief chemist for a major oil and gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average in excess of 4.2 ounces of this ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline? .0062 .0753 .4013 .0475Suppose there is a random variable X whose probability density function has the form (shown in image). a) Find P(X>-0.2) b) Find the 90th percentileQuestion 1) Suppose the travel time from White Plains Transit Center to SUNY WCC on public transit (Bus Route #15) follows a Uniform Distribution with a minimum time of 10 minutes and maximum time of 25 minutes. Let the random variable x represent the time from White Plains Transit Center to SUNY WCC on public transit. What is the probability Density Function, pdf, for the random variable x? Sketch the Density Curve for the random variable x. What is the probability the travel time is between 15 and 20 minutes? What is the probability the travel time is between 10 and 13 minutes?