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- Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 228 numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1.(i) Test the claim that p is more than 0.301. Use ? = 0.10 (a) What is the value of the sample test statistic? (Round your answer to two decimal places.) (b) Find the P-value of the test statistic. (Round your answer to four decimal places.)It is known that the average lifetime of a central processing unit (CPU) of a server is eight years and shows an exponential distribution. What is the probability that the company that leases the server for five years will encounter a central processing unit (CPU) failure within the lifetime? a)0.465 b)0.395 c)0.535 d)0.606 e)no oneA maker of soft-drinks is considering the introduction of a new brand. He expects to sell 50,000 to 1.00,000 bottles of its soft drink in a given period according to the following probability distribution: 50 60 70 80 90 100 No. of Bottles sold (in '000) : Probability If the product is launched he will have to incur a fixed cost of would give him a profit of 0-13 0-20 0-35 0-22 0-08 0-02 48,000. However, each bottle sold 1-25. Should he introduce the new brand?
- The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20-39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size n = 500 of young adults ages 20-39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, X, in Lance's sample who regularly skip breakfast is greater than 122. You may find table of critical values helpful. Express the result as a decimal precise to three places. P(X > 122)%3D eal limir thaor tnr the hinamialdietrikotian tn indtha neohabilin: tbot the numbar of individuale in Aanly tha nd tems of use contact us he p about us cyeers 6:56 PM 11/6/2020 a. 2) Cip prt sc insert 110 |Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 87 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. 1) Test the claim that p is more than 0.301. Use α = 0.10. 2) What is the value of the sample test statistic? (Round your answer to two decimal places.) 3) Find the P-value of the test statistic. (Round your answer to four decimal places.) 4) If p is in fact larger than 0.301, it would seem there are too many numbers in…If you know that every 30 minutes, a plane takes off from Jeddah Airport to Riyadh Airport, starting at 10 am. If a group of passengers arrives at Jeddah airport at a time that follows the regular continuous distribution between 6:00 a.m. and 7:30 a.m., then what is the likelihood that passengers wait for the plane less than 15 minutes
- 10. The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 15 minutes. a. What is the probability that there are no calls within a 30- minute interval? b. What is the probability that at least one call arrives within a 10-minute interval? c. What is the probability that the first call arrives within 5 and 10 minutes after opening? d. Determine the length of an interval of time such that the probability of at least one call in the interval is 0.90The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?Q3 a) A component has an exponential time to failure with a mean of 100 hours. (i) The component has already been in operation for its mean life. What is the probability that it will fall by 150 hours? (ii) The component will operate for another 50 hours given that it is in operation 150 hours. (iii) If 20 components are tested, what is the probability that at least one fails in less than 200 hours? Assume that the components fail independently. b) Students of National University were classified according to their favorite color: Blue 12 5 Favorite color Red 13 13 Black 25 20 Male Female If one student is selected at random, then find the probability that the selected student: (i) Doesn't like black color. (ii) Is Female and likes blue color. (iii) Is Male or like black color. (iv) Likes red color given that it is female.
- Sell 50,000 to 1,00,000 bottles of its soft drink in a given period according to the following probability distribution : 25-6. A maker of soft-drinks is considering the introduction of a new brand. He expects to 60 70 80 90 100 50 No. of Bottles sold (in '000) : Probability 0-20 0-35 0-22 0.08 0.02 0-13 I the product is launched he will have to incur a fixed cost of Rs. 48,000. However, each bottle sold give him a profit of Rs. 1-25. Should he introduce the new brand ? WouldWhat is the difference between discrete and continuous probability distributions? What are six situations in which a variable of interest may be considered either continuous or discrete?indicate the units to the final answer if any Draw the necessary graph if any. Round off to four decimal places or in lowest term if your answer is in fraction.
