The distribution for the length of a persons tongue is norma

The distribution for the length of a person’s tongue is normally distributed. A random sample of 4 people had an average of 6.3 inches with a standard deviation of 1.2 inches. Find a 95% confidence interval for the true average length of a tongue.

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    6.3          
t(alpha/2) = critical t for the confidence interval =    3.182446305          
s = sample standard deviation =    1.2          
n = sample size =    4          
df = n - 1 =    3          
Thus,              
              
Lower bound =    4.390532217          
Upper bound =    8.209467783          
              
Thus, the confidence interval is              
              
(   4.390532217   ,   8.209467783   ) [ANSWER]