Problem 7 A mall is promoting an event of sales. Every $10 a customer spends can get a fortune ticket. Each ticket has a chance of 0.08 to win a gift. How much should a customer spend, so that the probability of getting at least one gift is 0.95. Perform our calculation use normal approximation with continuous correction.
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- It takes a while for new factory workers to master a complex assembly proces. During thre first month new employees wor, the company tracks the number of days the have been on the job and the length of time it rtakes them to complete assembly. The correlation is most likely to be what?Please use excel formulas when possible: You have a device that uses a single battery, and you operate this device continuously, never turning it off. Whenever a battery fails, you replace it with a brand new one immediately. Suppose the lifetime of a typical batteryhas an exponential distribution with mean 205 minutes. Suppose you operate the device continuously for three days, making battery changes when necessary. Find the probability that you will observe at least 25 failures. (Hint: The number of failures is Poisson distributed.) In the previous problem, we ran the experiment for a certain number of days and then asked about the number of failures. In this problem, we take a different point of view. Suppose you operate the device, starting with a new battery, until you have observed 25 battery failures. What is the probability that at least 15 of these 25 batteries lived at least 3.5 hours? (Hint: Each lifetime is exponentially distributedPreviously, De Anza's statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. Find the probability that an individual had between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.
- If the duration of a disease is long and the incidence of the disease is low, the prevalence rate of that disease will be similar to the incidence rate of that disease. True FalseTwo geysers that are near to each other are labelled as Geyser A and Geyser B. The time between eruptions for a given geyser follows an exponential distribution. The eruption times of the two geysers are independent of one another. The mean amount of time between eruptions of Geyser A is 39 minutes, and the mean amount of time between eruptions of Geyser B is 66 minutes. Given that exactly one of the geysers erupts within the next 49 minutes, determine the probability that it will be Geyser A. O 0.6654 0.7850 O 0.7252 O 0.6953 O 0.7551Please solve within 30 minutes. Suppose the number of hurricanes N in a given year is Poisson distributed with a mean of 4. Losses Xi due to individual hurricanes is exponentially distributed with a mean of 1,000. Let X denote the total loss due to the N hurricanes. Find Var(X).
- A mail order company has an 8% success rate. If it mails advertisements to 502 people, find the probability of getting less than 34 sales. Round z -value calculations to 2 decimal places and final answer to at least 4 decimal places. P(X<34)=A recent survey of 1040 U.S. adults selected at random showed that 634 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.Step 1Recall that the probability of an event based on relative frequency uses the formulaprobability of event = relative frequency = fn,where f is the frequency of the event occurrence in a sample of n observations. A total of 1040 people were surveyed and 634 considered the occupation of firefighter to have very great prestige. Therefore, the sample size is n = . The event of interest is that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige. Therefore, the frequency f is equal to the number of adults who the occupation of firefighter has very great prestige, so f = (0.6096 answer is incorrect.) .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. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
- The probability that at a filling station one has to wait more than 7 minutes for the service is 0.14. Given the waiting time is exponentially distributed find the probability that we are served in 3 minutes after arrival.Suppose ₁ and ₂ are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 9, x = 113.3, s₁=5.01, n = 9, y = 129.6, and s₂ = 5.34. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.) USE SALT -21.57 1x ) Does the interval suggest that precise information about the value of this difference is available? Because the interval is so narrow, it appears that precise information is available. Because the interval is so narrow, it appears that precise information is not available. Because the interval is so wide, it appears that precise information is available. Because the interval is so wide, it appears that precise information is not available. x -11.06