Our favorite deity has informed us that the true mean of x is 0 and its true standard deviation is 5.
How small would x have to be such that 97.5% of X's are larger? (Show work)
Mean(x) = 0
standard deviation =s(x) = 5
Find x such that, P[X > x ] = 97.5% = 0.975
Also, we know that
P[ Z > -1.96 ] = 0.975





P[X > -9.8 ] = 97.5% = 0.975
Our favorite deity has informed us that the true mean of x is 0 and its...
The serum cholesterol levels for 20-24 year old males in the US has mean 180 mg/100ml and standard deviation σ = 46 mg/100ml. We are interested in the mean cholesterol level of the larger population of 20-74 old males, say µ. Suppose, we have a random sample of size 25 from the larger population. We want to test the following hypotheses at significance level α = 0.01: H0 : µ = 180, HA : µ > 180 a) What is...
Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $30 and the estimated standard deviation is about $5. (a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount...
True or false: Consider two normal curves. If the first one has a larger mean than the second one, then it also has a larger standard deviation than the second one. true false
Suppose x has a distribution with a mean of 30 and a standard deviation of 12. Random samples of size n = 64 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has ---Select--- an approximately normal a normal a Poisson a geometric a binomial an unknown distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 33. z = (c) Find P(x...
Suppose x has a distribution with a mean of 50 and a standard deviation of 27. Random samples of size n = 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 41. z = (c) Find P(x < 41). (Round your answer to four decimal places.) P(x < 41)...
Suppose an x distribution has mean μ = 5. 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 > 6.25) smaller? Explain your answer. The distribution...
4. Let us suppose that twenty-five textbooks for 2000-level courses had a mean cost of $124. (a) Report an appropriate 99% confidence interval estimate for the mean cost of all 2000-level textbooks, write out the full procedure taught in this class. We'll assume that the prices of all 2000-level textbooks vary with standard deviation $100. (b) Based on your confidence interval, would $180 be a reasonable estimate of the population mean cost? (c) If we used a lower confidence level...
Suppose x has a distribution with a mean of 90 and a standard deviation of 3. Random samples of size n = 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has ---Select--- a normal a geometric an unknown a Poisson a binomial an approximately normal distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 91. z = (c) Find P(x...
Suppose x has a distribution with a mean of 90 and a standard deviation of 21. Random samples of size n = 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution has ---Select- distribution with meanz - and standard deviation o, - (b) Find the z value corresponding to x = 83. ZE (c) Find P(x < 83), (Round your answer to four decimal places.) P(x < 83) = (d) Would...
Consider a random experiment that has as an outcome the number x. Let the associated variable be X, with true (population) and unknown probability density function fx(x), mean ux. and variance σχ2. Assume that n-2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes xi and x2 Let estimate μ X of true mean #xbe μχ = (x1+x2)/2. Then the random variable associated with estimate μ xis estimator random 1. a. Show the...