Part IV: Sections 5.5-5.717.Suppose that the number of defects in a randomly selectedone carat diamond of a certain type follows a Poisson distribution withX= 3.By the Central Limit Theorem, what is the approximate(a)distribution of the mean number of defects in the random sample of 40one carat diamonds? You should give a name for the distribution, as welltwo associated numerical quantities.(b)the random sample of 40 one carat diamonds, the probability that thesample mean number of defects is less than y is less than 98%.Estimate the largest number of defects y such that in

Solution: Let X represent the number of defects in a randomly selected one carat diamond of a…

Answered: Part IV: Sections 5.5- 5.7 17. Suppose…

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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5. Fifteen male economists are in a life raft with a maximum carrying capacity of 2850 pounds. The distribution of weights of male economists is normal with a mean of 178 pounds and a standard deviation of 17 pounds. (a) Find the probability that a randomly chosen economist weighs more than 189 pounds. (b) Find the probability that a randomly chosen economist weights between 180 and 190 pounds. (c) Find the lower bound of average weight of the economists beyond which the boat will be overloaded. (d) Find the probability that the average weight of the 15 economists exceeds the lower bound of average you calculated in part c.
-5. The weight of a certains species of fish is normally distributed with mean of 4.25 Kg and standard deviation of 1.2 a) What proportion of fish are between 3.5 kg and 4 kg b) What is the probability that a fish caught will have a weight of at least 5kg? 31
3. (Normality Test, p, If it is possible to obtain a large number of observations for a variable X, a histogram would be helpful to determine whether or not X has approximately a normal distribution. However, if the sample is small (size < 30), a quantile-quantile plot is suggested. (1) po, For the following sample, calculate the z quantiles z,, z,,, Z, (n=12), which divide the area under z-curve to 13 equal parts. 0.06 0.11 0.12 0.12 0.13 0.17 0.19 0.20 0.23 0.25 0.29 0.31 1 3 4 5 8 10 11 12 0.0769 0.1538 0.2308 0.3077 0.3846 0.4615 0.5385 0.6154 13 0.7692 0.8462 0.9231 0.6923 (2) sample was taken from a normal population. Draw a q-q plot (plot (x1, z,), (x2, z,), ., (x12, Z12 )) to determine whether or not the
23. A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 24 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.08 seconds. At α=0.10 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state H0 and Ha. H0: muμ less than or equals≤ 14.814.8 Ha: muμ greater than> 14.814.8 (Type integers or decimals. Do not round.) The claim is the alternative hypothesis. (b) Use technology to find the P-value. Find the standardized test statistic, t. t=1.651.65 (Round to two decimal places as needed.) Obtain the P-value. P=0.0560.056 (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null…
8. In the UK (United Kingdom) Baby Birth weight can be approximated by a Normal Distribution with N(3.39, 0.55) with numbers being in kg (kilograms) D. Compute P(birth weight > 4 kg) using a normal distribution calculator E. Compute the Z-Score for a 2 kg birth F. Compute P(birth weight < 2 kg) using a normal distribution calculator
2. The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes, Draw the area under the curve and find the probability that a call a. Lasts between 5 and 10 b. Lasts more than 7 minutes c. Lasts less than 4 minutes
3. The mass of coffee in a randomly chosen jar sold by a certain company may be taken to have a normal distribution with means 203 g and standard deviation 2.5g. (i) Find the probability that a randomly selected jar will contain at least 200g of coffee. Obtain the probability that two randomly selected jars will together contain between 400g and 405g of coffee. (iii) The random variable ī denotes the mean mass (in grams) of coffee per jar in a random sample of 20 jars. Identify the value of a such that P(T – 203| < a) = 0.95. (ii)
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We have a Poisson distribution for cacti with a mean of 280 per square kilometer. They are asking for the mean of cacti per 10,000 square meters. They are telling us that 1 square kilometer = 1,000,000 square meters. My confusion is on converting the units. When they say 280 per square kilometer, are they saying 280 divided by square kilometer? I've attached an image of my work. My professor said that the answer is 2.8.
17. A 20,000-piece manufacturing run of 2200 resistors has a mean value of 2200 (naturally!) and a standard deviation of 2.50. They are to be sold as a 2% tolerance product, which means that the values must be between 0.98 x220 N = 215.60 and 1.02 x 220 0 = 224.40.
Complete the given relative frequency distribution and compute the stated relative frequencies. (a) P({1, 3, 5}) Step 1 Outcome 1 Rel. Frequency 0.1 0.2 (b) P(E) where E = {1, 2, 3} (a) P({1, 3, 5}) 2 Outcome 1 0.1 2 4 We are given the incomplete relative frequency distribution. 3 0.1 5 4 5 Rel. Frequency 0.1 0.2 0.1 0.1 The missing table value is the relative frequency value corresponding to the outcome 0.5 X 5

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