The length of time for one patient to be treated in a clinic is a random variable having a mean of 7 patients per hour.

1. What is the probability the first patient arrives within 5 and 10 minutes after opening?
2. What is the probability that there NO patients in 20 minutes time.
3. What is the probability that there are at least 4 patients within 30 minutes?

The grade appeal process at a university requires that a jury be structured by selecting

eight

individuals randomly from a pool of

eight

students and

twelve

faculty.​ (a) What is the probability of selecting a jury of all​ students? (b) What is the probability of selecting a jury of all​ faculty? (c) What is the probability of selecting a jury of

four

students and

four

​faculty?

Peter and Paul bet $1 on each game. Both players start with $10. Peter is extremely nervous on the first game, and the probability of him winning that game is only 1/4. After that, his probability of winning any given game is back to 5/8. Under these circumstances, what is the probability that Peter bankrupts Paul?

The grade appeal process at a university requires that a jury be structured by selecting six individuals randomly from a pool of eight students and thirteen faculty.​ (a) What is the probability of selecting a jury of all​ students? (b) What is the probability of selecting a jury of all​ faculty? (c) What is the probability of selecting a jury of three students and three ​faculty?

In a region, 12% of the adult population are smokers, 0.8% are smokers with emphysema, and 0.2% are non-smokers with emphysema.

a. What is the probability that a person selected at random has emphysema?

b. Given that the selected person is a smoker, what is the probability that the person has emphysema?

c. Given that the selected person is not a smoker, what is the probability that this person has emphysema?

1. What is the probability of having exactly 10 days of precipitation in the month of April in West Palm Beach? If it only rain about 3.66 inches in the month of April.
2. What is the probability of having less than three days of precipitation in the month of April?
3. What is the probability of having more than 15 days of precipitation in the month of April?

Identify the parameter n in the following binomial distribution scenario. A weighted coin has a 0.441 probability of landing on heads and a 0.559 probability of landing on tails. If you toss the coin 19 times, we want to know the probability of getting heads more than 5 times. (Consider a toss of heads as success in the binomial distribution.)

QUESTION 4: The returns for an asset are normally distributed. The mean return is 9.75% and the standard deviation is 3.25%. a. What is the probability of earning a negative return? (3 points) b. What is the probability of earning a return between 6.5% and 16.25%? (3 points) c What is the probability of earning a return greater than 13%? (3 points)

A class in probability theory consists of 3 men and 5 women. An exam is given, and the students are ranked according to their performance. Assuming that no two students obtain the same score, and all rankings are considered equally likely.

1.The probability that women receive the bottom 5 scores is

2.The probability that the top grade and the bottom grade are for men is