Although the first quarter of 2002 was quite dismal on Wall Street, mutual funds investing in gold companies rose an average of 35.2%. Assume that the distribution of returns in the first quarter of 2002 for mutual funds specializing in gold companies is fairly symmetrical with a mean of 35.2% and a standard deviation of 20%. If random samples of 16 gold stock funds were selected:

Complete Question

Although the first quarter of 2002 was quite dismal on Wall Street, mutual funds investing in gold companies rose an average of 35.2%. Assume that the distribution of returns in the first quarter of 2002 for mutual funds specializing in gold companies is fairly symmetrical with a mean of 35.2% and a standard deviation of 20%. If random samples of 16 gold stock funds were selected:

 90% of the sample mean returns are between what two values symmetrically distributed around the mean?

The two values symmetrically distributed around the mean  are  

   21.87\%   and  43.17\%

Step-by-step explanation:

From the question we are told that

   The sample size is  

  The sample  mean is  

    The standard deviation is  

Generally the degree of freedom is mathematically represented as

=>  

=>  

From the question we are told the confidence level is  90% , hence the level of significance is    

=>  

Generally from the t distribution table the critical value  of   at  a degree of freedom of  is  

Generally the margin of error is mathematically represented as  

=>      

=>      

Generally 90% confidence interval is mathematically represented as  

=>  

converting to percentage

=>      

Hence   the 90% of the sample mean returns are between 21.87\%  and 43.17\%

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step-by-step explanation: