Find the mean and standard deviation of the following observations : X:1, 2, 4, 6, 8, 9 Transform the given observations such that : (i) The mean of the transformed series becomes 12 while the standard deviation remains unchanged. (ii) The mean of the transformed series becomes 12 and standard deviation becomes double the standard deviation of the given series.
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- Two resistors, with resistances R1 and R2, are connected in series. R1 is normally distributed with mean 100Ω and standard deviation 4Ω, and R2 is normally distributed with mean 120Ω and standard deviation 10Ω. What is the probability that R2 exceeds R1 by more than 30 Ω?Two resistors, with resistances R1 and R2, are connected in series. R1 is normally distributed with mean 100 Ω and standard deviation 5 Ω,and R2 is normally distributed with mean 120 Ω and standard deviation 10 Ω. a) What is the probability that R2 > R1? b) What is the probability that R2 exceeds R1 by more than 30 Ω.Which of the following is/are FALSE about the central limit theorem? A. The CLT says that as the sample size nn increases to infinity, the sample mean converges to the population mean, given that the population mean and variance are finite. B. The CLT explains why the binomial distribution will approximately be normally distributed when nn is large. C. The CLT says that at a large sample size nn, the sample mean will be approximately normal with mean equal to the population mean and variance equal to the population variance divided by the sample size nn , given that the population mean and variance are finite. D. The CLT guarantees that all natural phenomena are normally distributed. E. The CLT is used in the derivation of the sampling distribution of the sample mean for hypotheses tests such as zz-test or tt-test. F. A and B G. C and D H. A and D I. B and E
- A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 105.6 90.9 91.2 96.9 96.5 91.3 100.1 105.5 99.6 107.7 103.3 92.4 Does this data suggest that the population mean reading under these conditions differ from 100? (a) State the null and alternative hypotheses. (b) Calculate, correct to 2 decimal places, (i) the sample mean, x ; and (ii) the sample standard deviation, s. (c) Evaluate the appropriate test statistic. (d) Test these hypotheses at 0.05 level of significance.Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 73.7 Q2 82.5 Q3 108.1 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,733 Time 65.8 If the original value of the series in a Q4 was 2,197, then what is the seasonally adjusted value?In the following questions, random samples of the given size are drawn from populations with the given means and standard deviations. For each question, a) find the mean and standard error of the distribution of differences in sample means (x⎯⎯⎯1−x⎯⎯⎯2x¯1−x¯2), b) indicate if the sample size is large enough for the Central Limit Theorem to apply. Give your answers to 4 decimal places. Samples of size 80 from Population 1 with mean 16 and standard deviation 5.6 and samples of size 20 from Population 2 with mean 18 and standard deviation 9.5. Mean: Std. Error: Is the sample size large enough for the Central Limit Theory to apply?i. Yes ii. No Samples of size 1000 from Population 1 with mean 36 and standard deviation 8.5 and samples of size 1000 from Population 2 with mean 28 and standard deviation 6.7. Mean: Std. Error: Is the sample size large enough for the Central Limit Theory to apply?i. Yes ii. No Samples of size 30 from Population 1 with mean 36 and standard…
- Two populations are surveyed using simple random samples. A sample of size n1 is used for population I, which has a population standard deviation of σ 1, and a sample of size n2 = 2n1 is used for population II, which has a population standard deviation σ 2 = 2 σ 1. For which of the two samples would you expect the sample mean to be more accurate?Suppose x has a distribution (not nessarily normal) with mean 50 and standard deviation 8. According to the Central Limit Theorem, which of the following is true? For samples of size n = 16, is normal with mean 50 and standard deviation 1. For samples of size n = 64, is normal with mean 50 and standard deviation 1. For samples of size n = 16, is normal with mean 50 and standard deviation 8. For samples of size n = 64, is normal with mean 50 and standard deviation 8.A company has 9000 arrivals of Internet traffic over a period of 18,050 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)= (μ^x • e^−μ) / x! to find the probability of exactly 2 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
- Suppose the time until your iPhone breaks is uniformly distributed between 0 and 8 years. You will get a new phone as soon as your iPhone breaks or at time 2 (when a new iPhone is released), whichever is first. Find the standard deviation for the time until you get a new phone.1. 0.622. 0.553. 0.494. 0.525. 0.57A sample is selected from a population with μ = 50 and σ = 12. If the sample mean of M = 56 produces a z-score of z = +1.00, then how many scores are in the sample?If X is a uniformly distributed random varibale with a=2 and b=6, then Calculate the standard deviation of X? Round to three decimal places