Please show each step working out the problem and getting to the answer!!
Question 1
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 18 applicants:
At least 6 will be accepted?
Exactly 10 will be accepted?
Exactly 5 will be rejected?
Fifteen or more will be accepted?
Determine the expected number of acceptances.
Compute the standard deviation.
Question 2
Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6.
What is the probability that a randomly selected exam will have a score of at least 71?
What percentage of exams will have scores between 89 and 92?
If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?