Question 1 Seventy percent of the students applying to a university are accepted. Using the binomial probability tables or Excel, what is the...

Seventy percent of the students applying to a university are accepted. Using the binomial probability tables or Excel, what is the probability that among the next 12 applicants:

1. At least 6 will be accepted?
2. Exactly 10 will be accepted?
3. Exactly 8 will be rejected?
4. Seven or more will be accepted?
5. Determine the expected number of acceptances.
6. Compute the standard deviation. 

Scores on a recent national statistics exam were normally distributed with a mean of 90 and a standard deviation of 5.

1. What is the probability that a randomly selected exam will have a score of at least 85?
2. What percentage of exams will have scores between 89 and 92?
3. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?