An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.4 years of the population mean. Assume the population of ages is normally distributed. ​(a) Determine the minimum sample size required to construct a 90​% confidence interval for the population mean. Assume the population standard deviation is

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An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within
1.4
years of the population mean. Assume the population of ages is normally distributed.
​(a) Determine the minimum sample size required to construct a
90​%
confidence interval for the population mean. Assume the population standard deviation is
1.6
years.
​(b) The sample mean is
20
years of age. Using the minimum sample size with a
90​%
level of​ confidence, does it seem likely that the population mean could be within
9​%
of the sample​ mean? within
10​%
of the sample​ mean? Explain.
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(b) The
90​%
confidence interval is
​(18.0
 
18.0​,
22.0
 
22.0​).
It
 
does not seem
seems
likely that the population mean could be within
9​%
of the sample mean because the interval formed by the values
9​%
away from the sample mean
 
entirely contains
overlaps but does not entirely contain
the confidence interval. It
 
seems
does not seem
likely that the population mean could be within
10​%
of the sample mean because the interval formed by the values
10​%
away from the sample mean
 
entirely contains
overlaps but does not entirely contain
the confidence interval.
​(Round to two decimal places as​ needed.)
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