1.

In the game of blackjack as played in casinos in Las Vegas, Atlantic City, Niagara Falls, as well as many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 0.29. Find the probability that an average player wins

A. twice in 5 hands.

Probability =

B. 11 or more times in 26 hands.

Probability =

There are several books that teach blackjack players the "basic strategy" which increases the probability of winning any hand to 0.43. Assuming that the player plays the basic strategy, find the probability that he or she wins

C. twice in 5 hands.

Probability =

D. 11 or more times in 26 hands.

Probability =

2.

A game of chance involves rolling an unevenly balanced 4-sided die. The probability that a roll comes up 1 is 0.2, the probability that a roll comes up 1 or 2 is 0.51, and the probability that a roll comes up 2 or 3 is 0.46 . If you win the amount that appears on the die, what is your expected winnings? (Note that the die has 4 sides.)

3.

The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.9 per week. Find the probability of the following events.

A. No accidents occur in one week.

Probability =

B. 3 or more accidents occur in a week.

Probability =

C. One accident occurs today.

Probability =

Code Using Arrays in Java

There is a new ruling for the only elevator located at Block B. Students who need to ride the elevator, must line up in a queue. The rated load in pounds for the elevator is based on the inside net platform areas. The maximum load for the elevator is 500 pound.

Write a program to read the students weight (in pound) in the line and calculate the number of students that are allowed to enter the elevator before it makes a loud noise.

Input

The first line of input is T (1 ≤ T ≤ 100) which is the number of test case. This is followed by T lines of input. Each line starts with X (X ≤ 100) which is the number of students who want to ride the elevator. This is then followed by a list of X data which is the students’ weight in the line.

Output

For each test case, the output contains a line in the format "Case #x: y", where x is the case number (starting from 1) and y indicates the number of students in the line that are allowed to ride the elevator.

Sample Input

3
9 45 25 50 46 10 55 50 83 68
5 66 155 93 101 90 
8 64 70 50 45 85 74 110 95 

Sample Output

Case #1: 9
Case #2: 4
Case #3: 7

19. Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (c) below.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 70 beats per minute and 78 beats per minute.

The probability is _____

​(Round to four decimal places as​ needed.)

b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 70 beats per minute and 78 beats per minute.

The probability is____

​(Round to four decimal places as​ needed.)

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

A.Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

B.Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size.

C.Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size.

D.Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.

20. An elevator has a placard stating that the maximum capacity is 2310 lb -15 passengers. ​ So, 15 adult male passengers can have a mean weight of up to 2310 divided by 15 equals 154 pounds. If the elevator is loaded with 15 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 154 lb.​ (Assume that weights of males are normally distributed with a mean of 163 lb and a standard deviation of 31 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is_____

​(Round to four decimal places as​ needed.)

Does this elevator appear to be​ safe?

A.No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.

B.Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity.

C.Yes, 15 randomly selected people will always be under the weight limit.

D.No, 15 randomly selected people will never be under the weight limit.

A department store elevator is moving downward in a multistory building at a constant speed of 6.30 m/s. Exactly 2.04 s after the top of the elevator car passes a bolt loosely attached to the wall of the elevator shaft, the bolt falls from rest.

(a)

At what time (in s) does the bolt hit the top of the still-descending elevator? (Assume the bolt is dropped at

t = 0 s.)

(b) Estimate the number of floors through which the bolt can fall if the elevator reaches the ground floor before the bolt hits the top of the elevator. (Assume

1 floor = 3 m.)

Q2. Consider a game of tennis from deuce onward. Starting at the state of deuce, if the server wins, the score is ad-in. If the server then loses the next point, the game is back to deuce. However, if the server wins two points in a row, he wins the game. Similarly, starting at the state of deuce, if the returner wins, the score is ad-out. If the returner then loses the next point, the game is back to deuce. But if the returner wins two points in a row, he wins the game.

Let the probability of winning the point be 0.4. Moreover, the winner gets $10, and the loser pays $10.

1. Is this game recursive?

2. Draw and properly label the game tree. If there is a state that recurs, do not go beyond that state.

3. What is the probability of winning the game in the state of deuce?

4. What is the probability of winning the game for the server given that he wins the first point after deuce?

What is the value of the game at the state of deuce?

An elevator has a placard stating that the maximum capacity is 1344 lblong dash8 passengers.​ So, 8 adult male passengers can have a mean weight of up to 1344 divided by 8 equals 168 pounds. If the elevator is loaded with 8 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 168 lb.​ (Assume that weights of males are normally distributed with a mean of 170 lb and a standard deviation of 32 lb​.) Does this elevator appear to b

An elevator has a placard stating that the maximum capacity is 1610 lblong dash10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1610 divided by 10 equals 161 pounds. If the elevator is loaded with 10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 161 lb.​ (Assume that weights of males are normally distributed with a mean of 171 lb and a standard deviation of 28 lb​.) Does this elevator appear to be​ safe?

An elevator has a placard stating that the maximum capacity is 2565 lb/15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2565 divided by 15 equals 171 pounds. If the elevator is loaded with 15 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 171 lb.​ (Assume that weights of males are normally distributed with a mean of 179 lb and a standard deviation of 27 lb ​.) Does this elevator appear to be​ safe?

An elevator has a placard stating that the maximum capacity is 1328 lb--8 passengers. So, 8 adult male passengers can have a mean weight of up to 1328/8=166 pounds. If the elevator is loaded with 8 male passengers, find the probability that it is overloaded because they have a mean weight greater than 166 lb. (Assume that weights of males are normally distributed with a mean of 173 lb and a standard deviation of 29 lb.) Does this elevator appear to be safe?

Two players (player A and player B) are playing a game against each other repeatedly until one is bankrupt. When a player wins a game they take $1 from the other player. All plays of the game are independent and identical. a) Suppose player A starts with $2 and player B starts with $1. If player A wins a game with probability p, what is the probability that player A wins all the money? b) Suppose player A starts with $6 and player B starts with $6. If player A wins a game with probability 0.5, what is the probability the game ends (someone loses all their money) on exactly the 10th play of the game?