4. Let X₁,..., Xn be n random samples of a normal distribution X~ N(μ, 300) where μ is unknown. What sample size n is required such that the width of the 97 percent confidence interval is barely larger than 5?
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- A population has a mean µ = 161 and a standard deviation o = 20. Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 56. The mean is = μx (Round to three decimal places as needed.) and the standard deviation is o- = X 3 XSuppose an x distribution has mean μ = 2. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81. (a) What is the value of the mean of each of the two x distributions? For n = 49, μ x = For n = 81, μ x = (b) For which x distribution is P( x > 2.5) smaller? Explain your answer. The distribution with n = 49 because the standard deviation will be smaller.The distribution with n = 81 because the standard deviation will be smaller. The distribution with n = 49 because the standard deviation will be larger.The distribution with n = 81 because the standard deviation will be larger. (c) For which x distribution is P(1.5 < x < 2.5) greater? Explain your answer. The distribution with n = 49 because the standard deviation will be larger.The distribution with n = 49 because the standard deviation will be smaller. The distribution with n = 81 because the standard deviation will be…suppose the random variable X has a normal distribution with a mean of 10 and a variance of 256 calculate the following: P(12 < x < 20 ) USE DECIMAL VALUES AND ROUND OFF FINAL ANSWER TO TWO DECIMAL PLACES!
- 3. If Z is a random variable having the standard normal distribution, find i. P(Z - 1.08) iii. P(-1.90A random sample of n= 4 is obtained from a normal distribution μ=30, σ=8. What is the probability the sample mean will be smaller than M = 22? Report to the thousandthsX is a normally distributed random variable with a mean of 5.00 and a standard deviation of 11.39. If the right area is 0.4716 then what is the value of X?4. Let X be a random variable representing dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation = 2.4%. A random sample of 19 Australian bank stocks has a sample mean of = 8.71%. For the entire Australian stock market, the mean dividend yield is = 5.9%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.9% ? Use Q=.05. Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis? A. The p-value is less than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis. B. The p-value is less than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis. C. The p-value is greater than the level of significance and so the data are statistically significant. Thus, we fail to reject the…A population of v alues has a normal distribution with μ=48.2 and σ=93.1You intend to draw a random sample of size n=232. Find the value separating the bottom 89% values from the top 11% values. Find the sample mean separating the bottom 89% sample means from the top 11% sample means.A population of values has a normal distribution with μ=244.4 and σ=50. You intend to draw a random sample of size n=148.Find P37, which is the mean separating the bottom 37% means from the top 63% means.P37 (for sample means) = Enter your answers as numbers accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.Suppose x has a distribution with mean 22 and standard deviation 16. If a random sample of size n=36 is drawn find p(22<×<24)Suppose we have the short hand info on a Normal Distribution as N(10,25). What is the population mean of the distribution and what is the population standard deviation? μ = σ =A random sample of size 16 is taken from a normal distribution with population variance 2.56 and sample mean is 130, find the margin error for 95% confidence interval of population mean a. 1.784 O b. 1.254 O . 0.784 O d. 0.194