9. The number of customers who visit a car dealer's showroom on a Saturday morning is arandom variable with mean 18 and standard deviation 2.5. With what probability can we assertthat:a) There will be more than 13 but fewer than 23 customers? Show your reasoning.Chebyshev's Theorem must be used for this.18-k(2.5)=13k=2P(13=1-- 0.0.89k=+3.01511a = 10.46b=25.54

Answered: 9. The number of customers who visit a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1.If the cosmic radiation to which a person is exposed while flying by jet across US is a random variable having mean 4.35 mrem and standard deviation 0.59 mrem,find the probabilities that the amount of cosmic radiation to which a person will be exposed on such a flight is (a)Between 4.00 and 5.00 mrem (b)At least 5.50 mrem (c)Less than 4.00 mrem
5. A loss random variable X has a Pareto distribution and e = unspecified. If with d = 2 (100) 5 e, (50) 3 ex determine TVAR, (x) when p= 48/49. %3D
2. Traffic accidents at a particular intersection follow a Poisson distribution with an average rate of 1.4 accidents per week. (Hint: Let X represent "the number of days before the next accident occur" X follows what kind of distribution? You should not expect to use this[r.v. for all the parts below) a) What is the probability that the next accident will not occur for three days? b) What is the probability that the next accident will happen within the next day?
10. The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 6 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period.e. Calculate the probability that there will be a failing student within the first semester.f. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?
3. A survey on a random sample of 1000 farmers shows that 17% of them spend more than S700 per year on seeds. Assume the population proportion is p =.17. Show the sampling distribution of p, the sample proportion of farmers spending more than $700 per year on seeds. What is the probability that the sample proportion will be within +.02 of the population proportion'? Answer part (b) for a sample of 1600 households. d. e. f.
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23. *An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day for each day of hospitalization thereafter. The number of days of hospitalization, X, is a discrete random variable with probability function Pr(X = k) = (1/15)(6 – k), k = 1, 2, 3, 4, 5. Calculate the expected payment for hospitalization under this policy. (213.3)
9. This is a simplified inventory problem. Suppose that it costs c dollars to stock anitem and that the item sells for s dollars. Suppose that the number of items thatwill be asked for by customers is a random variable with the frequency functionp(k). Find a rule for the number of items that should be stocked in order tomaximize the expected income. (Hint: Consider the difference of successiveterms.)
32 - The random variable X, which shows the grades of the students in a class in the exam of the statistics course, has a normal distribution with a mean of 80 and a variance of 25. Which of the following is the lowest grade with a probability of 0.3015? a) 32.5 B) 55 NS) 82.5 D) 68 TO) 89
a) Turkey is the most tea-loving country in the world. In 2014, the annual per capita consumption of tea in Turkey, denoted X, was normally distributed with a mean of 6:96 lb and a standard deviation of 2:36 lb. b)You pick a random sample of 5 people from Turkey (assume all of them are tea drinkers) and compute their mean per capita tea consumption to be only 3:98 lb. (i) What is the probability that her random sample has an average of 3:98 lb or lower, when the population average is as given above? (ii)Recall that a large sample size makes it unlikely thatthe sample mean is too far away from the population mean. How big a samsle should you have to draw so that the standard deviation of your sample average is less than 10% of its mean (i.e., less than 0.696 lb)?
How was 7.5 obtained?

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