SOLUTION: QUESTION:The management of saving centre has calculated mean of 42 saving accounts rs 75000 and standard deviation rs 10000 .conclude that would it be responsible that the populati

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Question 1136831: QUESTION:The management of saving centre has calculated mean of 42 saving accounts rs 75000 and standard deviation rs 10000 .conclude that would it be responsible that the population means is less than rs 100000 by using 5 % significance level.?/
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
it is almost 100% certain that the population mean will be less than 100,000.

in fact, at 95% confidence level, it is most likely that the population mean will be less than 78,024.

i used the following online distribution calculator.

http://davidmlane.com/hyperstat/z_table.html

here are the results of my inquiries.

you needed to find the standard deviation of the distribution of sample means of size 42.

that formula is s = standard deviation / square root of sample size.

you get s = 10,000 / sqrt(42) = 1543.034 rounded to 3 decimal places.

the first display shows that the probability of the population mean being less than 100,000 is 100%.

the second display shows that the probability of the population mean being less than 78,024 is about 97.5%.

bottom line is that there is a 0% probability that the population mean will be greater than 100,000.