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.
b.) Find the probability all 20 children recognize their mother's voice.
c.) Let the random variable x denote the number of children who do not recognize their mother's voice. Find the mean of x.
d.) Let the random variable x denote the number of children who do not recognize their mother's voice. Find the variance of x.