Answer:
a) The 90% confidence interval would be given (0.561;0.719).
b) 
c) Using the significance level assumed  we see that
 we see that  so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion is higher than 0.5 or 50%.
 so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion is higher than 0.5 or 50%.    
Step-by-step explanation:
1) Data given and notation  
n=100 represent the random sample taken    
X=64 represent were in favor of firing the coach
 estimated proportion for were in favor of firing the coach
 estimated proportion for were in favor of firing the coach
 is the value that we want to test since the problem says majority
 is the value that we want to test since the problem says majority    
 represent the significance level (no given, but is assumed)
 represent the significance level (no given, but is assumed)    
z would represent the statistic (variable of interest)    
 represent the p value (variable of interest)
 represent the p value (variable of interest)    
p= population proportion of Americans for were in favor of firing the coach
Part a
The confidence interval would be given by this formula
 
For the 90% confidence interval the value of  and
 and  , with that value we can find the quantile required for the interval in the normal standard distribution.
, with that value we can find the quantile required for the interval in the normal standard distribution.
 
And replacing into the confidence interval formula we got:
 
 
And the 90% confidence interval would be given (0.561;0.719).
Part b
We need to conduct a hypothesis in order to test the claim that the proportion exceeds 50%(Majority). :    
Null Hypothesis:  
  
Alternative Hypothesis:  
  
We assume that the proportion follows a normal distribution.    
This is a one tail upper test for the proportion of  union membership.  
The One-Sample Proportion Test is "used to assess whether a population proportion  is significantly (different,higher or less) from a hypothesized value
 is significantly (different,higher or less) from a hypothesized value  ".
".  
Check for the assumptions that he sample must satisfy in order to apply the test  
a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.  
b) The sample needs to be large enough  
 
  
 
  
Calculate the statistic    
The statistic is calculated with the following formula:  
 
  
On this case the value of  is the value that we are testing and n = 100.
 is the value that we are testing and n = 100.  
 
The p value for the test would be:  

Part c
Using the significance level assumed  we see that
 we see that  so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion is higher than 0.5 or 50%.
 so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion is higher than 0.5 or 50%.