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)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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. 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
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…
6. In a location two random samples were taken concerning the rate of hay fever per 1000 population. Sample 1 (n1 = 16) contained people under 25, sample 2 (n2 = 14) contained people over 50. %3D X1 = 109.5 S1 = 15.41 X2 = 99.36 s2 = 11.57 %3D Assume that the hay fever rate in each group has an approximately normal distribution. Do the data indicate that the over 50 group has a significantly lower hay fever rate? (Use a = 5%)
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)
8. People arrive at a farmer's market according to a Poisson process at rate 20 per hour. Suppose among them, 80% are type A who will shop elsewhere later; and 20% are type B who only buy produce at the farmer's market that day. Type A customers spend an average of $15 with a standard deviation of 8. Type B customers spend $30 with standard deviation of 10. In (i) and (ii) below you do not need to simplify your answers. (i) the probability that all these 5 arrive during the first hour? Condition on the event that there are 5 type B customers in the first two hours, what is (ii) arrive. Find the probability that in the first 30 min exactly two type A and two type B customers (ii) Find the mean and variance of Z. Let Z be the total amount of money spent at the market during the first three hours.
Consider sample data with x = 8 and s = 4. (a) Compute the coefficient of variation. what percent? (b) Compute a 75% Chebyshev interval around the sample mean.Lower Limit =Upper Limit=
2. The mass of beads filled into a package is (continuous) uniformly distributed between 220 and 226 grams. a. (10) Determine the mean and standard deviation of the mass of beads in a randomly chosen package. b. (15) What is the probability that a package is filled with less than the advertised target of 221 grams? c. (15) What is the mass of beads that is exceeded by 95% of the packages?
(a) Find the mean u and the standard deviation o for the collection of N = 8 stocks. (b) Find the sample mean i and sample standard deviation s of the random sample of stocks.
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.
(a) A distribution consists of three components with total frequencies of 200, 250 and'300 having mean 25, 10 and 15 respectively. Find the mean of combined distribution. (b) In a series with 100 items, having simple mean of 40, later on it was discovered that two items of 45, 35 were wrongly taken as 35 and 25. Find the correct mean. (c) A man travelled by auto for 3 days. He covered 480 kilometres each day. He drove the first day 10 hours @ 48 kilometres per hour, the second day 12 hours @ 40 kilometres per hour and third day 15 hours @ 32 kilometres per hour. What was his average speed ?
A population distribution has a mean of 40 and a standard deviation of 12. (a) What does the central limit theorem say about the sampling distribution of the mean ifsamples of size 50 are drawn from this population? (b) What is the probability that a random sample of 50 has a mean between 38 and 44?
24. A study compared union activity of employees in 10 plants during two different decades. The researchers reported “a significant increase in union activity, t ( 9 ) = 3.28 , p < .01. t ( 9 ) = 3.28 , p < .01. ” Explain this result to a person who has never had a course in statistics. Be sure to use sketches of the distributions in your answer.

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