document.write( "Question 372430: The distribution of survival time of guinea pigs with cancer after treatment is typically strongly right-skewed. Assume that the mean of the guinea pig survival time for a population of guinea pigs with cancer is 100 days with standard deviation of 10 days. Suppose we take a random sample of size n = 49 guinea pigs with cancer from the population of guinea pigs with cancer. What is the approximate probability that the sample mean survival time will be less than 95 days? \n" ); document.write( "

Algebra.Com's Answer #265301 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
By the Central limit theorem, the sampling distribution of the means is normally distributed with mean $\"mu+=+100\"$ days with standard deviation (or standard error of the mean) $\"sigma%2Fsqrt%28n%29+=+10%2Fsqrt%2849%29+=+10%2F7\"$ . Then

. (Note that the distribution of the underlying population need not be normal: the sample size is sufficiently large, and the sampling came from identical and independent distributions.) \n" ); document.write( "

\n" );