Displaying Data
Bivariate Data
Probability
100
Calculate the median distance travelled.
3km
100
Calculate Pearson's Correlation Coefficient for the following data.
0.991
100
A survey of 100 students shows:
60 students study Mathematics
45 students study Physics
25 students study both Mathematics and Physics
Find the probability that a randomly selected student studies math or physics.
0.8
200
Calculate the estimated mean height.
178cm
200
Use two words to describe the following correlation.
strong, negative
200
A survey of 100 students shows:
60 students study Mathematics
45 students study Physics
25 students study both Mathematics and Physics
Determine if the studying is math is independent from studying physics.
NO!
(Math AND Physics) = 25/100 = 0.25
P(Math) × P(Physics) = 0.60 × 0.45 = 0.27
OR
P(Physics | Math) = 25/60 ≈ 0.417
P(Physics) = 0.45
300
The following shows a 5 figure summary. Determine if 64 is an outlier.
YES!
(upper bound for outliers is 63)
300
Given the following data, (1, 15), (2, 18), (3, 22), (4, 25), (5, 28) find the equation of the regression line.
y = 3.30x + 11.7
300
A student takes two tests. The probability of passing each test is:
- P(pass Test 1) = 0.7
- P(pass Test 2) = 0.8
Find the probability they fail test 2, given that they passed test 1.
0.2
400
What distance is the 20th percentile?
2.1km
400
At Changi Airport in Singapore, six passengers were surveyed on the number of stores they had shopped in, and the waiting time for the flight, in minutes. Determine if it would be appropriate to use a regression model to estimate the number of stores with a given waiting time of 120 minutes. Explain why or why not.
No! 120 minutes is outside of the domain of the data (35 minutes to 75 minutes), therefore this is extrapolation and is not valid.
400
A box contains 5 red balls and 3 blue balls. Two balls are drawn without replacement.
What is the probability at least one red ball is drawn?
0.893
500
What percent of the group of children is at least 40 inches tall?
63.3%
500
The following table shows the total revenue, y, in US dollars (USD), obtained monthly during the first six months of 2020, by Law Office of Fox Brothers and the number of clients, x, served.
a) Find the equation of the regression line y on x.
b) Monthly operating cost for the law office is $2500. Additionally, the cost of serving each client is $200. Determine the profit when serving 6 clients in a particular month.
a) y = 654x - 541
b) Profit = -$700
500
A game involves spinning a spinner with 4 outcomes.
Red and Blue are each 2 times more likely than Green and Yellow. (Green and Yellow have equal probability)
The cost to play the game is $4. Determine if this is a fair game.
NO! E(x) = $1.33