1) [20 pts] Ruladsnerg is interested in exploring the relationship between the weight of a vehicle and its fuel efficiency. The scatter plot shows the data as weight ( in pounds) and fuel efficiency ( in miles per gallon- mpg) for a random sample of 5 vehicles:
a) Identify the explanatory and response variable and explain why. What are its units?
b) What would be a good correlation coefficient for the scatter plot? Choose one:
-0.97 or 1.2 or -1.4 or 0.03
c) If this can be classified as a linear relation, is it a positive relation or a negative relation or is there no relation?
d) If the linear relation equation may be expressed as y= 32.55 – 0.00448x, what would you predict would be the fuel efficiency for a car that weighs 2300 pounds?
e) Sensmirgrux’s car weighs more than Llojfuje’s car by 600 pounds. How could you compare the fuel efficiencies of the two cars?
2) [15 pts] The following table represents a tabulation of students enrolled in an online computer literacy education programme. No one can be in more than one class at a time. Please excuse the missing entries.
a) What is the probability that a randomly student is taking a course for credit?
b) What is the probability that a student is taking Database Management or Presentation Graphics?
c) Determine the probability that a student is taking a course for credit or Productivity Software?
3) [10 pts] In Five Card Poker a player is dealt five cards. Using a standard pack of cards, what is the probability that a player will be dealt five diamonds? What is the probability that a player is dealt five diamonds or five hearts?
4) [15 pts] The Agnubrabrunksiwx Insurance Group specialises in home insurance. Its basic policy costs $ 1200 for a year and it pays out $100,000 in case of fire damage to a home. According to The Insurer’s Almanac, the probability that a policy is paid out is XXXXXXXXXXWhat is the expected value for the The Agnubrabrunksiwx Insurance Group ?
5) [10 pts] A recent Gallop Poll indicates that 80 % of voting age adults disapprove of Congress. If 700 voting adults are chosen at random, what is the mean and standard deviation for the number of adults who disapprove of Congress? Out of a sample of 700 voters, would it be unusual to find 570 adults who disapprove of Congress?
6) [10 pts] Xewiurhanepsminitrop has determined that 35 % of viewers are tuned into Eyewitness News at 5 PM on Sunday evening. If 20 randomly selected television viewers are chosen, what is the probability that exactly 7 viewers are tuned into Eyewitness News at 5 PM on Sunday evening? What is the probability that at least 10 viewers are tuned into Eyewitness News at 5 PM on Sunday evening?
7) [20 pts] The zombie apocalypse has hit the fair town of Rukunhatserpxu! It is known that within a city block of our august town, the number of zombies is normally distributed with a mean of 100 zombies and a standard deviation of 20 zombies. What is the probability that within a city block the number of zombies is between 75 and 125? What is the probability that at least 70 zombies can be found on a given block? What is the probability that fewer than 85 zombies can be found on a given block?
XXXXXXXXXXAgents Allojfsneitinnerb and Billojfujsenunc attempt to smuggle secrets from the Grebnereab Military Establishment. If either agent fails in the mission he is never seen or heard from again. The probability of failure for stealing military secrets is 0.12. Would it be unusual for Allojfsneitinnerb to fail? Would it be unusual for both Allojfsneitinnerb and Billojfujsenunc to fail? What is the probability that at least one will succeed in stealing the secrets?
1. Frequency : A list of each category of data and the number of occurrences for each category of data.
1. Relative Frequency =
1. The sum of all the frequencies is the sample size: = n
1. The sum of all the relative frequencies is one: =1
1. µ = ( Population Mean)
1. x̅ = XXXXXXXXXXSample Mean)
1. s= ( Sample Standard Deviation)
1. σ = ( Population Standard Deviation)
1. IQR = Q3 – Q1 : Interquartile Range.
1. Lower fence = Q1– XXXXXXXXXXIQR)
1. Upper Fence = Q XXXXXXXXXXIQR)
1. Five Number Summary : Minimum, Q1 ,Q2 , Q3, Maximum.
THE LINEAR COEFFICIENT (THE PEARSON COEFFICIENT)
1. The linear coefficient, r, is always between -1 and 1 inclusive.
1. If r =1, then a perfect positive linear relation exists between the variables.
1. If r = -1, then a perfect negative linear relation exists between two variables.
1. The closer r is to + 1 the stronger is the evidence of a positive association between the variables.
1. The closer r is to -1 the stronger is the evidence of a negative association between the variables.
1. A value of r close to 0 implies little or no linear relation between the variables. There may be another relation, just not a linear one.
1. The correlation coefficient is not resistant.
The equation for the linear regression line (LSR) is
ŷ = b1 x + b0
Where the slope, b1 = r ( sy / sx ) and the y intercept b0 = ȳ- b1 x̄ .
r is the correlation coefficient
x̄ is the sample mean for the explanatory variable; sx is the sample standard deviation for the explanatory variable.
ȳ is the sample mean for the response variable; sy is the sample standard deviation for the response variable.
E is the event or an activity that has results.
XXXXXXXXXXProbability : P( E ) =
XXXXXXXXXXDisjoint or Mutually Exclusive: Events are disjoint or mutually exclusive if they have no common XXXXXXXXXXoutcomes.
XXXXXXXXXXFor disjoint events A and B:
XXXXXXXXXXP(A or B) = P(A) +P(B)
XXXXXXXXXXP(A or B) = P(A) +P(B) – P( A and B)
XXXXXXXXXXFor complementary Events A and : P(A) + P( =1
XXXXXXXXXXIndependence: Events A and B are independent if the occurrence of A has no effect on the occurrence of B and the occurrence of B has no effect on the occurrence of A.
XXXXXXXXXXFor independent events A and B : P( A and B) = P(A)P(B).
P( A and B) = P(A)P(B given A) .
The mean for a binomial discrete random variable is µ = np, where n is the number of trials or sample size and p is the probability of success.
The standard deviation of a binomial discrete random variable is σ =
The expected value or mean of a discrete random variable is E(x) = .
The Binomial probability may be calculated by the following formula: pk (1-p)n-k
1. Φ(z) = Probability or Proportion of values or Percentiles under certain conditions.
1. Raw score to z-scores: z=
1. Z-score to raw scores: x= zσ + µ or x= (An) σ + µ
where An= area under normal probability density curve.