A sample of 1138 adults conducted in 2016 asked "Do you mainly agree or disagree that your health has been improved thanks to research over the course of your lifetime?" We know the proportion p-hat...

A sample of 1138 adults conducted in 2016 asked "Do you mainly agree or disagree that your health has been improved thanks to research over the course of your lifetime?" We know the proportion p-hat of the sample who answer "somewhat agree" will vary in repeated sampling. in repeated sampling, the sample proportion, p-hat, has an approximately normal distribution with mean 0.45 and standard deviation 0.012.

(a) Find the probability that at least 0.474 of the random sample of 1138 adults somewhat agrees that health has been improved thanks to research over the course of their lifetime

(b) Find the probability that at most 0.438 of the random sample of 1138 adults somewhat agrees that health has been improved thanks to research over the course of their lifetime.

(c) Find the probabiity that between 0.431 and 0.469 of a random sample of 1138 adults somewhat agrees that health has been improved thanks to research over the course of their lifetime.

.887

I'm having trouble with a and b. Is C correct?