9) Suppose the average price of gasoline for a city in the United States follows a continuousuniform distribution with a lower bound of $3.50 per gallon and an upper bound of $3.80 pergallon. What is the probability a randomly chosen gas station charges more than $3.70 pergallon?

The lower bound is 3.50 and upper bound is 3.80.

Answered: 9) Suppose the average price of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify no private The ages of 25 are are respectively. Assuming that the distribution of ages is bell shaped, what percentage of the respondents will be between 64.3 and 93.4 years old? 61 89 65 90 69 92 76 70 73 60 67 75 64 82 68 73 66 76 86 74 62 81 63 68 81 approximately 83.9% approximately 60% O approximately 95% O approximately 81.5%
The average speeds of cars on a highway are distributed according to a normal distribution. Today, John is on his way to work. As he enters the highway, he notices a car speeding by at 150 km/hr. Ten seconds later, another car speeds by at 160 km/hr. John concludes that today, cars must be going faster for some reason. A few minutes later, John gets into a minor accident. Once again, he concludes that it was inevitable - he got into the accident because cars were driving faster today. Explain what fallacies - if any-are involved in both of John's claims. Is John justified in his conclusions?
Central Limit Theorem 2. According to the International Graduation Association, on average, high school girls in Canada spend $\$ 223.55$ on a prom dress with a standard deviation of $\$ 18.14$. If 76 high school girls are surveyed in Canada, what is the probability that the mean cost of their dresses is between $\$ 225.00$ and $\$ 228.00$ ? 3. It has been estimated that $23 \%$ of nurses are offered to work overtime on a regular basis. If we randomly selected 225 nurses, what is the probability that $25 \%$ or less of them will be offered overtime on a regular basis? SP.VS.717
State whether you would expect this distribution to be symmetric, left-skewed, orright-skewed, and briefly explain: ages of people obtaining a driver’s license for the firsttime.
The useful life of an electrical component is exponentially distributed with a mean of 4,000 hours. a. What is the probability the circuit will last more than 4,750 hours? b. What is the probability the circuit will last between 4,000 and 4,250 hours? c. What is the probability the circuit will fail within the first 3,750 hours?
4. The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 15 minutes. What is the probability that there are no calls within a 30-minute interval?
In 1995, the median price of a PC was $1200. Suppose that a random sample of100 persons who bought their PCs during that year recorded the amount spent (byeach of them) on his/her PC. State the approximate sampling distribution of ˆp, theproportion of persons who spent more than $1200 on a PC. Find the probabilitythat more than 60% of this group spent more than $1200. NOTE: Please explain each part, so the problem can be used as a Study Guide
in "a" the blank is "z" and "t" distribution
Which of the following distributions would be most likely to have a tail, and why? A. The GPAs of NMSU students, because some students have a 4.0. B. Class scores on a quiz, with 10 points possible, because the most common scores are 7, 8, and 9. C. The time it takes to install a new piece of computer software, because usually it’s quick, but occasionally it takes hours or even days. D. The amount of money you spend each month on food, because food prices change a little from day to day, and sometimes things are on sale.
e) Suppose that weekly household expenditures on petrol are normally distributed, with a mean of $120 and a standard deviation of $50. i. A family is randomly selected. Find the probability that this family spends more than $245 per week on petrol? A 2.5 B 0.0062 C 0.9938 D 0.0202 ii. The government wants to promote public transport and will award a prize to the families who spend the lowest amount on petrol. If the government only wants to give a prize to 10% of households, what is the most that a family is allowed to spend on petrol each week to obtain the prize? A $56 B $184 C $3.50 D $217.60 In a sample of 25 families, what is the probability that the average weekly expenditure on petrol will be less than $105? ii. A 0.0668 B 0.9332 C 0.3821 D 0.6179
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. 39.9 40.6 41.3 42 42.7 43.4 44.1 inches O -2.1-1.4 -0.7 0 0.7 1.4 2.1 inches O 10 14 18 22 26 30 34 (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) 0.8490 X inches 19.9 20.6 21.3 22 22.7 23.4 24.1 inches
4. A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. a. What is the distribution for the weights of one 25-pound lifting weight? What is the mean and standard deviation? b. What is the distribution for the mean weight of 100 25-pound lifting weights? c. Find the probability that the mean actual weight for the 100 weights is less than 24.9. 1 I

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9) Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $3.50 per gallon and an upper bound of $3.80 per gallon. What is the probability a randomly chosen gas station charges more than $3.70 per gallon?