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Evaluate $\lim _{x \rightarrow \infty}\left[\frac{1}{x} \cdot \frac{a^{x}-1}{a-1}\right]^{1 / x}$ where $a>0, a \neq 1$
In the last quarter of 2007, a group of 64 mutual funds had a mean return of 2.2% with a standard deviation of 6.5%. Consider the Normal model N(0.022, 0.065) for the returns of these mutual funds.a) What value represents the 40th percentile of these returns?b) What value represents the 99th percentile?c) What's the IQR, or interquartile range, of the quarterly returns for this group of funds?
A random sample of n = 25 is selected from anormal population with mean μ = 104 and standard deviation σ = 15.(a)Find the probability that x exceeds 111. (Round your answer to four decimalplaces.)(b)Find the probability that the sample mean deviates from thepopulation mean μ = 104 by no morethan 3. (Round your answer to four decimal places.)
Unemployment rate in a certain city stands at 30%. If a randomsample of 10 residents in this city is selected.Required:A.What is the probability that we get one unemployed person?B.What is the probability that we get at most two unemployedresidents? C.Find the mean and variance.
Suppose that the distance of fly balls hit to the outfield (inbaseball) is normally distributed with a mean of 267 feet and astandard deviation of 37 feet. Let X be the distance in feet for afly ball.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly hit fly ball travels lessthan 292 feet. Round to 4 decimal places. c. Find the 90th percentile for the distribution of distance of flyballs. Round to 2 decimal places. feet
2. The lengths of lumber a machine cuts are normally distributed with a mean of 105 inches and a standard deviation of 0.5 inch.(a) What is the probability that a randomly selected board cut by the machine has a length greater than 105.19 inches?(b) A sample of 38 boards is randomly selected. What is the probability that their mean length is greater than 105.19 inches?
Suppose that IQ is normally distributed with mean 90 andstandard deviation 10. Find the following.What is the probability that a randomly selected individual hasan IQ greater than 115?What is the probability that a randomly selected individual hasan IQ between 90 and 110?What is the probability that a randomly selected individual hasan IQ less than 105?What IQ is the 50th percentile for this population?What IQ is the 67th percentile for this population?a.0.933 b.0.477c.90d.94.4e.0.006
