Question

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.  Hint from Dr. Klotz: There are formulas you need on page 245 or check out 5.4 in Notations and Symbols for this week. Remember that standard deviation is the square root of the variance.

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?

Answer 1

[ The above probability is obtained using the function =1-BINOMDIST(5,12,0.7,TRUE) in Excel 07 which gives the value 0.961399 . ]

[ The above probability is obtained using the function =BINOMDIST(5,12,0.7,FALSE) in Excel 07 which gives the value 0.16779 . ]

[ The above probability is obtained using the function =BINOMDIST(4,12,0.7,FALSE) in Excel 07 which gives the value 0.16779 . ]

[ The above probability is obtained using the function =1-BINOMDIST(6,12,0.7,TRUE) in Excel 07 which gives the value 0.882151 . ]

.

.

.

[ The above probability is obtained using the function =1-NORMDIST(85,90,5,TRUE) in Excel 07 which gives the value 0.841345 . ]

[ The above probability is obtained using the function =NORMDIST(92,90,5,TRUE)-NORMDIST(89,90,5,TRUE) in Excel 07 which gives the value 0.841345 . ]

[ The above value is obtained using the function =NORMINV(0.975,90,5) in Excel 07 which gives the value 99.79982 . ]