The grades on an exam follow a skewed left distribution with a mean of 78% and a standard deviation of 18%. Is it safe to conclude that the shape of the sampling distribution of \bar{x} for samples of size 20 is normally distributed? A. Yes B. No Is it safe to conclude that the shape of the sampling distribution of \bar{x} for samples of size 36 is normally distributed? A. No B. Yes Describe the center and spread for the sampling distribution of \bar{x} for samples of size 36. $\mu_{\bar{x}} = $ (Give an exact answer.) $\sigma_{\bar{x}} = $ (Give an exact answer.) Compute the probability that a random sample of size 36 results in a mean score of 80% or higher. (Round to four decimal places.)
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The population distribution is skewed left with population mean μ = 78 and population standard deviation σ = 18. We will consider sampling distributions of the sample mean x-bar for n = 20 and n = 36. Show more…
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A random sample is drawn from a population with mean =57 and standard deviation =4.8.[You may find it useful to reference the z table.] a.ls the sampling distribution of the sample mean with n=14 and n=32 normally distributed?(Round the standard error to 3 decimal places.) n 14 32 Expected Value 57 57 Standard Error 1.283 0.849 b.Can vou conclude that the sampling distribution of the sample mean is normally distributed for both sample sizes? O Yes, both the sample means will have a normal distribution. O No,both the sample means will not have a normal distribution O No,only the sample mean with n=14 will have a normal distribution O No, only the sample mean with n = 32 will have a normal distribution. c.If the sampling distribution of the sample mean is normally distributed with n=14,then calculate the probability that the sample mean falls between 57 and 60. (If appropriate, round final answer to 4 decimal places.) O We cannot assume that the sampling distribution of the sample mean is normally distributed. O We can assume that the sampling distribution of the sample mean is normally distributed and the probability that the sample mean falls between 57 and 60 is Probability 0.4903
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