Where are the clusters in this distribution? 1400 1200 1000 800 600 400 200 ENS***&&&&&& O A. 7, 12, 17, 22, and 32 B. 17, 32, 47, and 62 O C. 32, 47, 62, 92 D. 17, 32, 47, 62, and 92 E. 72, 77, and 82
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- Use what you know about order statistics to show that for the random sample of size n = 3 the median is an unbiased estimator of the parameter θ of a uniform population with α = θ − 1/2 and β = θ + 1/2.A biologist needs to estimate the weight of all spiny lobsters on the Treasure Coast. To achieve this, the biologist collects a random sample of 20 spiny lobsters. The weights of each lobster in the sample are given below. Assume that the weights of all spiny lobsters on the Treasure Coast are normally distributed. 9.7 7.1 8.2 6.3 8.1 5.5 7.8 7.8 9.2 8.8 7.7 8.8 9.7 6.6 6.3 8.9 7 8.1 9 8.2 Determine the point estimate, ¯xx¯ and the sample standard deviation, ss. Round the solutions to four decimal places, if necessary.¯x=x¯=s=s=Using a 99% confidence level, determine the margin of error, EE, and a confidence interval for the average weight of a spiny lobster on the Treasure Coast. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.The margin of error is given by E=E=.A 99% confidence interval is given by .A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table on the right shows the day of the week for which 782 randomly selected fatal bicycle accidents occurred. At α=0.10,can you reject the claim that the distribution is uniform? Complete parts a through d below. Day Frequency, f Sunday 109 Monday 111 Tuesday 106 Wednesday 112 Thursday 121 Friday 106 Saturday 117 Question content area bottom Part 1 (a) State H0 and Ha and identify the claim. H0: The distribution of fatal bicycle accidents throughout the week is uniform not uniform Ha: The distribution of fatal bicycle accidents throughout the week is
- Photoresist is a light-sensitive material applied to semiconductor wafers so that the circuit pattern can be imaged on to the wafer. After application, the coated wafers are baked to remove the solvent in the photoresist mixture and to harden the resist. Here are measurements of photoresist thickness (in kÅ) for eight wafers baked at two different temperatures. Assume that all of the runs were made in random order. 95 ºC 100 ºC 11.176 5.623 7.089 6.748 8.097 7.461 11.739 7.015 11.291 8.133 10.759 7.418 6.467 3.772 8.315 8.963 (a) Is there evidence to support the claim that the higher baking temperature results in wafers with a lower mean photoresist thickness? Use = 0.05. (b) What is the P-value for the test conducted in part (a)? (c) Find a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval.These questions concerns the following situation. There is a rain on a football ground. The ground is 100 meters long and 70 meters wide. Model the event of a raindrop falling as a randomly selected point in the rectangle pictured.Lets imagine the following random variables: X is the x-coordinate where a raindrop falls, Y is the y-coordinate of where a raindrop falls, and Z=X+Y. CHOOSE ONE AND SHOW THE PROCESS. Which one of the following statements about the joint cumulative distribution function F(a,b) = P(X<a, Y<b) is false? * a) If 0 ≤ a ≤ 100 and 0 ≤ b ≤ 70 then F(a,b) = ab/7000 b) F(200,200) = 1 c) F is normally distributedA cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.a. How many customers would you expect to see, on average, at the coffee urn?b. How long would you expect it to take to get a cup of coffee?c. What percentage of time is the urn being used?d. What is the probability that three or more people are in the cafeteria?e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constanttime of 15 seconds, how does this change your answers to (a) and (b)?
- Distribution of first digits (Benford's Law) Digit 1 2 3 4 5 Probability 0.301 0.176 0.125 0.097 0.079 Digit 6 7 8 9 Probability 0.067 0.058 0.051 0.046 First digits in allegedly fraudulent checks First digit 1 2 3 4 5 6 7 8 9 Frequency 36 25 28 20 23 17 15 17 77 The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 188 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. a) What is the test statistics? b) What is the p-value?1-) It has been determined that the distribution of faulty products in a factory conforms to Poisson. 2% of the products produced monthly are defective. Calculate the probability of finding 5 defective parts in 400 randomly drawn samples.a. 0.091b. 0.140c. 0.253D. 0.145e. 0.085A biologist needs to estimate the weight of all Spanish lobsters on the Treasure Coast. To achieve this, the biologist collects a random sample of 20 Spanish lobsters. The weights of each lobster in the sample are given below. Assume that the weights of all Spanish lobsters on the Treasure Coast are normally distributed. 6.2 4 5.8 4.5 5.1 6.8 6.1 6.5 4.6 5.2 5.3 6.3 4.5 5.1 6.4 4.4 4.5 6 4.1 4.1 Determine the point estimate, x¯ and the sample standard deviation, s. Round the solutions to four decimal places, if necessary.x¯=s=Using a 99.9% confidence level, determine the margin of error, E, and a confidence interval for the average weight of a Spanish lobster on the Treasure Coast. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.The margin of error is given by E=. *I just need the nswr for s and E
