Chapter 6. 1 Quizzes
Joe the barber charges $32 for a shave and haircut and $20 for just a haircut. Based on experience, he determines that the probability that a randomly selected customer comes in for a shave and haircut is 0.85, the rest of his customers come in for just a haircut. Let J =what Joe charges a randomly-selected customer. a). Give the probability distribution for J.
(J, P(J)): {20, 0.15} {32, 0.85}
Man Hong is running the balloon darts game at the school fair. He has blown up hundreds of balloons with notes about prize tickets inside them. Twelve percent of the notes say "You win 5 tickets," twenty percent say "You win 3 tickets," and the rest say "Sorry, try again!" After each play, he replaces the popped balloon with another one bearing the same note. Let T = the number of tickets won by a randomly selected player of this game. a). Give the probability distribution for T.
(T, P(T)): {0, 0.68} {3, 0.20} {5, 0.12}
The probability distribution below is for the random variable X = number of medical tests performed on a randomly selected outpatient at a certain hospital. (X, P(X)): [0, 0.33] [1, 0.20] [2, 0.18] [3, 0.14] [4, 0.12] [5, 0.03] a).Make a histogram of this probability distribution in the grid
1). Number 1 through 5 on the x- axis 2). Number 0. 1 through 0. 3 on the y- axis 3). Graph
The probability distribution below is for the random variable X = number of mice caught in traps during a single night in small apartment building. (X, P(X)): [0, 0.12] [1, 0.20] [2, 0.31] [3, 0.14] [4, 0.16] [5, 0.07] a). make a histogram of probability distribution in the grid
1). Number 1 through 5 on the x- axis 2). Number 0. 1 through 0. 3 on the y- axis 3). Graph
A four sided die, shaped like an asymmetrical tetrahedron, has the following roll probabilities. (Number on die, Probability): [1, 0.4] [2, 0.3] [3, 0.2] [4, 0.1] Let X = the result of a single roll d). Find the smallest value A for which P(X < A) > 0.6
P (X < 3) = 0.4 + 0.3, so A = 3.
A four sided die, shaped like an asymmetrical tetrahedron, has the following roll probabilities. (Number on die, Probability): [1, 0.4] [2, 0.3] [3, 0.2] [4, 0.1] Let X = the result of a single roll a). Find P(1 < x < 4)
P( 1 < X < 4) = P(X=2 or X=3) = 0.3 + 0.2 = 0.5
A four sided die, shaped like an asymmetrical tetrahedron, has the following roll probabilities. (Number on die, Probability): [1, 0.4] [2, 0.3] [3, 0.2] [4, 0.1] Let X = the result of a single roll b). Find P( X ≠ 3)
P( X ≠ 3) = 1- P(X=3) = 1 - 0.2 = 0.8
The mean height of players in the National Basketball Association is about 79 inches and the standard deviation is 3.5 inches. Assume the distribution of heights is approximately Normal. Let H = the height of a randomly-selected NBA player. Find and interpret P(H > 74) .
P(H > 74) = P(Z > (74-79)/3.5)) = P(z > - 1.43) = 0. 9236 This is the probability that a randomly selected NBA player's height is greater than 74 inches.
The total sales on a randomly-selected day at Joy's Toy Shop can be represented by the continuous random variable S, which has a Normal distribution with a mean of $3600 and a standard deviation of $500. Find and interpret P(S > $4000 ).
P(S > $4000) = P{ z > (4000- 3600/500)} = P(z > 0.8) = 0. 2119 This is the probability that the total sales on a randomly-selected day exceeds $4000.
As of December 2008, various polls indicate that 35% of people who use the internet have profiles on at least one social networking site. We will discover later in the text that if you take a sample of 50 internet users, the proportion of the sample who have profiles on socialnetworking sites can be considered a random variable. Moreover, assuming the 35% is accurate, this random variable will be approximately Normally distributed with a mean of 0.35 and a standard deviation of 0.067. What is the probability that the proportion of a sample of size 50 who have profiles on social networking sites is greater than 0.5?
P(X > 0.5) = P(z > (0.5-0.35)/0.067) = P(z > 2.24) = 0.0125
The probability distribution below is for the random variable X = number of mice caught in traps during a single night in small apartment building. (X, P(X)): [0, 0.12] [1, 0.20] [2, 0.31] [3, 0.14] [4, 0.16] [5, 0.07] c). Express the event "trapping at least one mouse" in terms of X and find its probability.
P(x ≥ 1)= 0.88
The probability distribution below is for the random variable X = number of medical tests performed on a randomly selected outpatient at a certain hospital. (X, P(X)): [0, 0.33] [1, 0.20] [2, 0.18] [3, 0.14] [4, 0.12] [5, 0.03] c). Express the event "performing at least two tests" in terms of X and find its probability.
P(x ≥ 2) = 0.47
A four sided die, shaped like an asymmetrical tetrahedron, has the following roll probabilities. (Number on die, Probability): [1, 0.4] [2, 0.3] [3, 0.2] [4, 0.1] Let X = the result of a single roll e). If T = sum of two rolls, find P(T=4).
The event T = 4 can happen three ways: {1, 3}, {3, 1}, and {2, 2}. Probabilities for these events are, respectively, (0.4) (0.2)= 0.08; (0.2) (0.4)= 0.08; and (0.3) (0.3)= 0.09. Hence the total probability is 0.25.
A four sided die, shaped like an asymmetrical tetrahedron, has the following roll probabilities. (Number on die, Probability): [1, 0.4] [2, 0.3] [3, 0.2] [4, 0.1] Let X = the result of a single roll c). Describe P(x=3 |x ≥ 2 ) in words and find its value.
The probability of rolling a 3, given that the roll is 2 or greater; 0.2/0.6= 1/3
The probability distribution below is for the random variable X = number of medical tests performed on a randomly selected outpatient at a certain hospital. (X, P(X)): [0, 0.33] [1, 0.20] [2, 0.18] [3, 0.14] [4, 0.12] [5, 0.03] b). Describe P(X ≤ 3) in words and find its value
The probability that an outpatient undergoes no more than 3 medical tests; 0.85.
The probability distribution below is for the random variable X = number of mice caught in traps during a single night in small apartment building. (X, P(X)): [0, 0.12] [1, 0.20] [2, 0.31] [3, 0.14] [4, 0.16] [5, 0.07] b). Describe P(X ≥ 2) in words and find its value
The probability that two or more mice are caught during a single night; 0.68.
Man Hong is running the balloon darts game at the school fair. He has blown up hundreds of balloons with notes about prize tickets inside them. Twelve percent of the notes say "You win 5 tickets," twenty percent say "You win 3 tickets," and the rest say "Sorry, try again!" After each play, he replaces the popped balloon with another one bearing the same note. Let T = the number of tickets won by a randomly selected player of this game. b. Find and interpret the mean of T, μT .
μT: the mean number of tickets won per contestant in the long run = 0(0.68)+ 3(0.2)+ 5(0.12)= 1.2 tickets
A four sided die, shaped like an asymmetrical tetrahedron, has the following roll probabilities. (Number on die, Probability): [1, 0.4] [2, 0.3] [3, 0.2] [4, 0.1] Let X = the result of a single roll f). Find and interpret the mean and standard deviation of X.
μX: 1(0.4) + 2(0.3) + 3(0.2) + 4(0.1) =2 σX: √(.4(1-2)^2+ .3(2-2)^2 .2(3-2)^2+ .1(4-2)^2)=1 μX: is the expected mean roll if the die is rolled many times, or the expected long-run value of a single roll σX: is the variability in the number rolled in the long run
Joe the barber charges $32 for a shave and haircut and $20 for just a haircut. Based on experience, he determines that the probability that a randomly selected customer comes in for a shave and haircut is 0.85, the rest of his customers come in for just a haircut. Let J =what Joe charges a randomly-selected customer. (b) Find and interpret the mean of J, μJ .
μj= the mean amount of money Joe can expect to make per customer in the long run = 20 0.15 32 0.85 $30.20.
Man Hong is running the balloon darts game at the school fair. He has blown up hundreds of balloons with notes about prize tickets inside them. Twelve percent of the notes say "You win 5 tickets," twenty percent say "You win 3 tickets," and the rest say "Sorry, try again!" After each play, he replaces the popped balloon with another one bearing the same note. Let T = the number of tickets won by a randomly selected player of this game. c). Find and interpret the standard deviation of T,σT.
σT: the average distance from the mean (1.2) for each individual contestant √(0.68(0- 1.2)^2+ .2(3-1.2)^2+ .12(5-1.2)^2) = 1.833 tickets
Joe the barber charges $32 for a shave and haircut and $20 for just a haircut. Based on experience, he determines that the probability that a randomly selected customer comes in for a shave and haircut is 0.85, the rest of his customers come in for just a haircut. Let J =what Joe charges a randomly-selected customer. c). Find and interpret the standard deviation of J, σJ.
σj: the average distance from the mean ($30.20) for each individual customer √(.15(20-30.20)^2+ .85(32-30.20)^2) = $4.28
