I got them all wrong can someone please help me thank you Ar

I got them all wrong, can someone please help me! thank you!

Are you helping to save the environment? A USA Today Snapshot found that about 78% of Americans believe that recycling trash makes the biggest difference In protecting the environment. Suppose a random sample of n = 40 adults are polled and asked if they believed that recycling made the biggest difference in protecting our environment. Let us assume that the 78% figure is, in fact, correct. What are the probabilities for the following events? (Round your answers to four decimal places.) (a) Fewer than 26 individuals believe that recycling makes the biggest difference? (b) More than 33 individuals believe that recycling makes the biggest difference? (c) More than 7 individuals believe that recycling does not make the biggest difference?

Solution

Normal Approximation to Binomial Distribution
Mean ( np ) =40 * 0.78 = 31.2
Standard Deviation ( npq )= 40*0.78*0.22 = 2.6199
Normal Distribution = Z= X- u / sd                   
a)
P(X < 26) = (26-31.2)/2.6199
= -5.2/2.6199= -1.9848
= P ( Z <-1.9848) From Standard NOrmal Table
= 0.0236                  
b)
P(X > 33) = (33-31.2)/2.6199
= 1.8/2.6199 = 0.687
= P ( Z >0.687) From Standard Normal Table
= 0.246                  
c)

Mean ( np ) =40 * 0.22 = 8.8
Standard Deviation ( npq )= 40*0.22*0.78 = 2.6199
Normal Distribution = Z= X- u / sd                   
P(X > 7) = (7-8.8)/2.6199
= -1.8/2.6199 = -0.687
= P ( Z >-0.687) From Standard Normal Table
= 0.754