Need help Im stuck can someone help me set this up A Gallup

Need help, I\'m stuck, can someone help me set this up.

A Gallup Poll showed that 47% of Americans are satisfied with the way things are going in the United States. Suppose a sample of 25 Americans are selected.

Find the probability that no more than 7 Americans are satisfied with the way things are going.

Find the probability that more than 35% but at most 60% of these Americans are satisified with the way things are going.

Solution

A)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    25      
p = the probability of a success =    0.47      
x = the maximum number of successes =    7      
          
Then the cumulative probability is          
          
P(at most   7   ) =    0.042499437 [answer]

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b)

Note that the standard error of the population proportion is

sp = sqrt[ p ( 1 - p) / n] = sqrt(0.47*(1-0.47)/25) = 0.099819838

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    0.35      
x2 = upper bound =    0.6      
u = mean =    0.47      
          
s = standard deviation =    0.099819838      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.202165846      
z2 = upper z score = (x2 - u) / s =    1.302346333      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.11464964      
P(z < z2) =    0.90360099      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.788951351   [ANSWER]