Math help please- I've done most the work for you and provided my answers/justification?

Question

I need homework help! No, I am not cheating. I have provided my answers below. I just need to know if I did them right. And if I didn't, can you tell me what I did wrong? Please help. Thank you.

6.	From past experience it is known that 90% of one-year old children can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 20 one-year olds is given this voice recognition test.

a.)	Find the probability at least 3 children do not recognize their mother’s voice. (2 points)
b.)	Find the probability all 20 children recognize their mother’s voice. (2 points)
c.)	Let the random variable x denote the number of children who do not recognize their mother’s voice. Find the mean of x. (2 points)
d.)	Let the random variable x denote the number of children who do not recognize their mother’s voice. Find the variance of x. (2 points)

MY ANSWERS:::
a) 3 or more failing = 3-2/sqrt1.8 = z score of 1.51 = .9345 = 1-.9345 = 
ANSWER OF .0655

b) 0-2/sqrt1.8 = z score of -1.49 = 
ANSWER OF .0681

c) ANSWER OF mean = 2?

d) (1-.9)(9^2) =
ANSWER OF .1236

David · Accepted Answer

.9 can recognize
.1 can't

at least 3 don't recognize is the same as 
1 - (0, 1 or 2 don't recognize)
P(0) = .1^20
P(1) = (20c1) * .1 * .9^19
P(2) = (20c2) * .1^2 * .9^18

P(0 + 1 + 2) = 0.55535015059889674771
P(x>=3) =  1 - 55.54%
44.46%

all 20 = .9^20 = 0.12157665459056928801
12.16%

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Math help please- I've done most the work for you and provided my answers/justification?

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