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In: Statistics and Probability

A group of 100 of the 2,500 students enrolled in a college in natural sciences reveals...

A group of 100 of the 2,500 students enrolled in a college in natural sciences reveals that 35 are 17 years old, 45 are 18 years old, 10 are 19 years old, 6 are 20 years old, three are 21 years old and one is 22 years old.

a)provide an estimate for the mean, variance and standard deviation for the Age of the group.

b) Find the confidence interval with a confidence bands of 90% , 95% , and 99% by approximating the sample as having been taken with replacement

c) Find the same confidence intervals as in b), but treat the sample as taken without replacement.

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