Confidence interval and normal distribution

Question

For question (a), is the answer 0.7143?

For question (b), is the answer 10.85 and 11.95 ?

Answer 1

For the first problem, note that $9$ months is $1.5$ standard deviation units below the mean. From a table of the standard normal, we can see that the pobability that $Z\gt -1.5$ is approximately $0.9332$. Call this number $p$.

If the probability of "success" is $p$, then the probability of $9$ or more successes in $10$ trials is $$\binom{10}{9}p^9(1-p)+\binom{10}{10}p^{10}(1-p)^0.$$ The calculator gives an answer substantially larger than yours.

We have not verified your second computation.