2.) According to the central limit theorem the sampling distribution for a sample mean X? should be normally distributed. Given the random variable X represents the test score for a given student in a given class and has population mean ?x = 75 and standard deviation ?x = 15. a.) What is the mean and standard deviation for the sampling distribution of X? if it is the average of n = 4 tests? ?x? = **** ?x? = **** b.) What is the probability that the student taking n = 4 tests will receive a C or better average? P(70 ? X?) = ****
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We want to find the mean and standard deviation for the sampling distribution of the sample mean (X̄) when the sample size is n. According to the Central Limit Theorem, the mean of the sampling distribution of the sample mean (X̄) is equal to the population mean Show more…
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According to the central limit theorem, the sampling distribution for the sample mean X should be normally distributed. Given that the random variable X represents the quiz score for a given student in a given class and has a population mean µ = 75 and standard deviation σ = 15, what is the mean and standard deviation for the sampling distribution of X if it is the average of n = 16 quizzes?
Adi S.
According to the central limit theorem, the sampling distribution of the sample mean is approximately: A. normal B. standard normal C. t distributed D. f distributed 2. A population consists of 14 observations. If the sample size is fixed at 4 and the order is not important, the total number of possible samples using a simple random sampling method is: A. 24040 B. 1001 C. 1000 D. 3632428800 3. X follows a normal distribution with a mean of 20 and a variance of 4. When p=0.75, X is: A. 7.45E-07 B. 21.35 C. 3.14E-22 D. 22.70 4. P(-1 < z < 2.5) is: A. 0.9938 B. 0.8413 C. 0.8351 D. 0.1525
Rosina D.
All possible samples of size 20 are taken from a population and the mean is computed for each sample. The mean of the sample means a) is equal to the square root of the sample variance. b) is less than the population mean c) is equal to the population mean d) can be any number Which of the following pairs of parameters is sufficient to define a specific normal curve? a) The mean and the standard deviation. b) The range and the standard deviation. c) The mean and the z-score. d) None of the above. Assume scores on a recent national statistics exam were normally distributed with a mean of 74 and a standard deviation of 6. a) Find the probability that a randomly selected student score more than 77 points? b) A random sample of 50 statistics students is selected. What is the probability that the mean score of this sample is more than 77 points? A sample of size 42 will be drawn from a population with mean 52 and standard deviation 9. a) Why is it appropriate to use the normal distribution to find probabilities for x (sample means)? b) Find the 55th percentile of x.
Frank D.
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