document.write( "Question 1177196: 1. A survey reports its results by stating that standard error of the mean to be is 20. The population standard deviation is 500.
\n" ); document.write( "(i). How large is the sample used in this survey?
\n" ); document.write( "(ii). What is the probability that the sample mean will be within 25 of the population mean?
\n" ); document.write( "2(a). The time it takes a fire department to respond to a request for emergency aid has a mean of 14 minutes with standard deviation of 4 minutes. Suppose we randomly sample 50 emergency requests over a two-month period.
\n" ); document.write( "(i). State the sampling distribution of the sample mean, ̅x.
\n" ); document.write( "(ii). What is the probability that the sample mean will be 15 minutes or less?
\n" ); document.write( "(iii). What role does the Central Limit Theorem play in identifying this distribution?
\n" ); document.write( "(b). A population has a mean of 400 and a standard deviation of 50. The probability distribution of the population is unknown. A research study will use a simple random sample of either 10, 20, 35, or 50. items to collect data about the population.
\n" ); document.write( "(i). In which of these sample sizes will you be able to use the Normal probability distribution to describe the sampling distribution of the sample mean, ̅x. Explain.
\n" ); document.write( "(iii). Determine the standard error of the sampling distribution of ̅x for the instances where the Normal distribution would be appropriate.
\n" ); document.write( "(iii). What theorem would you appeal to for the justification of your answers in (i) and (ii). State it.
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Algebra.Com's Answer #805504 by ewatrrr(24785) $\"\"$ $\"About$

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document.write( "Hi\r\n" );
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document.write( "!.   = 20\r\n" );
document.write( "i.  = (500/20)^2 = 625\r\n" );
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document.write( "ii. ME = =25\r\n" );
document.write( "   25 = z*20\r\n" );
document.write( "   z = 25/20 = 1.25  and P (z ≤  1.25) = .8944\r\n" );
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document.write( "2a.   \r\n" );
document.write( "       1/SE = z =  1.7678  and P(z ≤  1.7678) = .9615\r\n" );
document.write( "The central limit theorem states that whenever a random sample of size n is taken from any distribution with mean and variance, then the sample mean will be approximately normally distributed with mean and variance\r\n" );
document.write( " We are proceeding as if the distribution of this sample(size 50)..its mean will be approximately normally distributed.\r\n" );
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document.write( "Will let You finish up or repost your last question.\r\n" );
document.write( "Site asks that there be one question per post.\r\n" );
document.write( "Wish You the Best in your Studies.\r\n" );
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