Probability Statistics (Question)

Question

The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds. Construct a 95% confidence interval for the population mean weight of newborn elephants. (Answer in 2 decimal places.) 

Answer: Blank 1 - Blank

Answer 1

244 + and - 11(1.96)/sqr50

= 244 - 3.05, 244+ 3.05

= (240.95, 247.05) is the 95% confidence interval

in general the confidence interval is mean - and + standard devation times z/sqr(n)

find z from a calculator or z table

for 95% the empirical rule gives a close but less accurate approximation of z =2

actual z value, accurate to 3 decimal places is 1.960

if you use that, the confidence interval is (244-11(2)/sqr50, 244+11(2)/sqr50)

or (240.89, 247.11) but that's slightly off, by 0.06