Answer:  The 90% confidence interval for the population mean μ is between 82.85 and 85.15,
Step-by-step explanation:
When population standard deviation is not given ,The confidence interval population proportion is given by ( ):-
 ):-
 
 
 , where n= Sample size.
s= Sample standard deviation
 = sample mean
 = sample mean
t* = Critical t-value (Two-tailed)
As per given , we have
  
 
n= 64
Degree of freedom : df = n-1=63  
s= 5.5
Significance level : 
Two-tailed T-value for df = 63 and   would be
 would be
 (By t-distribution table)
  (By t-distribution table)
i.e. t*= 1.669
The 90% confidence interval for the population mean μ would be
 
 
 
 
 
 

∴ The 90% confidence interval for the population mean μ is between 82.85 and 85.15,