Probability Distribution
In 2010, there were 1319 games played in the National Hockey League’s regular season. Imagine selecting one of these games at random and then randomly selecting one of the two teams that played in the game. Define the random variable X = number of goals scored by a randomly selected team in a randomly selected game. The table below gives the probability distribution of X.
Goals 0 1 2 3 4
Probability .061 .154 .228 .229 .173
The probability of 1 goal is
σ((X ± Y) ) = √(〖σX〗^2+ 〖σY〗^2 ) is
Which of the following random variables should be considered continuous?
a. The number of CD’s a randomly chosen person has
b. The number of sisters a randomly chosen person has
c. The number of goals scored in a randomly chosen soccer game
d. The number of tacos ordered by a randomly chosen Del Taco customer.
e. None of the above
5. In an experiment on the behavior of young children, each subject is placed in an area with five toys. Past Experiments have shown that the probability distribution of the number x of toys played with by a randomly selected subject is as follows:
Number of Toys 0 1 2 3 4 5
Probability .03 .16 .30 .23 .17 .11
What is the probability that the young child plays with at most two toys?
a. P(X=2) = .30
b. P(X<2) = .30
c. P(X ≤ 2) =.49
d. P(X ≤ 2) =.30
e. P(X > 2) =.49
5. Hanover High School has the best women’s swimming team in the region. The 400-meter freestyle relay team is undefeated. In the 400 meter freestyle relay, each swimmer swims 100 meters. The times, in seconds, for the four swimmers is approximately Normally distributed. If the mean of Wendy is 55.2 and the mean of Katie is 58, what is their combined mean?
6. A raffle sells tickets for $10 and offers a prize of $500, $1000, or $2000. Let C be random variable that represents the prize in the raffle drawing. The probability distribution of C is given below.
Value ci $0 $500 $1000 $2000
Probability pi 0.52 0.22 0.19 0.07
The expected profit when playing the raffles is
a. $430
b. $67,800
c. $80.42
d. $260.38
e. $440
It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens?
a.
0.961
b.
0.118
c.
0.882
d.
0.039
e.
0.079
A housing company builds houses with two-car garages. What percent of households have more than the garage can hold?
Number of Cars X 0 1 2 3 4 5
Probability .09 .36 .35 .13 .05 .02
The design of an electronic circuit for a toaster calls for a 100-ohm resistor and a 250-ohm resistor connected in series so that their resistances add. The components used are normally distributed. The resistance of a 100-ohm resistor has a a mean of 100 ohm and a standard deviation of 2.5 ohm, while that of 250 ohms resistors has a mean of 250 ohm and a standard deviation of 2.8 ohm.-60 . The combined mean of the total resistance of the two components in the series is
In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame can be adjusted to one of five different settings. The probability distribution is shown below:
Temperature 540 545 550 555 560
Probability .1 .25 .3 .25 .1
Which of the following is the expected value and the standard deviation?
a. Expected Value : 550 Degrees, Celsius Standard Deviation:5.7 degrees Celsius
b. Expected Value: 550 degrees Celsius, Standard Deviation:5 degrees Celsius
c. Expected Value:5 degrees Celsius, Standard Deviation: 10 degrees Celsius
d. Standard Deviation: 50 degrees Celsius, Expected Value: 5.7 degrees
e. Standard Deviation: 32.49 degrees Celsius, Expected Value: 5.7 degrees
Two percent of the circuit boards manufactured by a particular company are defective. If circuit boards are randomly selected for testing, the probability it takes 10 circuit boards to be inspected before a defective board is found is
a. .0167
b. .9833
c. 0.1829
d. 0.8171
e. The answer cannot be computed from the information given
Geometpdf(.02,10)
There is a 40% chance that students will attend the football game on Friday. Out of a group of 9 students, what is the probability that exactly 2 will attend the game?
Let the random variable X represent the number of telephone lines in use by the technical support center of a software manufacturer at noon each day. The probability distribution of X is shown in the table below.
X 0 1 2 3 4 5
P(X) 0.35 0.20 0.15 0.15 0.10 0.05
The P(X ≥ 4)
A time-and-motion study measures the time required for an assembly-line worker to perform a repetitive task. The data show that the time required to bring a part from a bin to its position on automobile chassis varies from car to car according to a normal distrubtion with a mean of 11 seconds and a standard deviation of 2 seconds. The time required to attach the part to the chassis follows a normal distribution with a mean of 20 seconds and a standard deviation of 4 seconds. The mean and standard deviation is
What is Mean of 31 seconds; Standard deviation of 4.4721
a. Find the expected number (mean number) of AP classes taken by the students. Interpret it.
X 1 2 3
P(X) .5 .4 .1
5. A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. Suppose the tennis player serves a random number of times.
Find the probability that she successfully serves 68 in a match of a total of 80 serves.
The amount of Lucky Charms in a randomly selected box has a mean of 9.70 ounces and a standard deviation of .03 ounces. Coco Puffs has a mean of a mean of 8.9 ounces and a standard deviation of .04 ounces. Assume both boxes are normally distributed and Bella buys one box of Lucky Charms and one box of Coco Puffs, what is the probability that the two boxes are greater than 18.4
A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. X had the following distribution:
X 1 2 3 4
Probability 0.2 0.4 0.3 0.1
Find (2 < X < 4)
Jonah likes sugar in his hot tea. From experience, he needs between 8.5 and 9 grams of sugar in a cup of tea for the drink to taste right. While making his tea one morning, Jonah adds four randomly selected packets of sugar. Suppose the amount of sugar in these packets follows a Normal Distribution with mean of 2.17 grams and standard deviation of .08 grams. The probability that Jonah’s tea tastes right is
A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make a profit of $5000 with probability 9/20, to break even with probability 5/20, and to lose $5000 with probability 3/20. The expected profit in dollars is
7. Which of the following random variables is geometric?
a. The number of times I have to roll a die
b. The number of cards I deal from a well-shuffled deck of 52 cards until I get a heart
c. The number of digits I read in a randomly selected row of the random digits table until I find a 7
d. The number of 7’s in a row of 40 random digits
e. The number of 6’s I get if I roll a die 10 times
A local club plans to invest $10000 to host a baseball game. They expect to profit $5000 with a probability of 80%. But if it rains on the day of game, they won't sell any tickets and the club will lose all the money invested. If the weather forecast for the day of game is 20%possibility of rain, is this a good investment?