The table shows the length, in km, of an Uber ride in New York City and the corresponc price, in USD, of the ride. Length in km (2) 5 8 10 13 16 20 25 Price in USD (y) 6.25 12.0 15.5 21.0 25.5 31.5 37.0 46.5 (a) Draw a scatter diagram for the above data on the axes below. Use a scale of 1 unit represent 2 km on the r-axis and 1 unit to represent 5 USD on the y-axis.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![The table shows the length, in km, of an Uber ride in New York City and the corresponding
price, in USD, of the ride.
Length in km (z)
8
10
13
16
20
25
Price in USD (y)
6.25
12.0
15.5
21.0
25.5
31.5
37.0
46.5
(a) Draw a scatter diagram for the above data on the axes below. Use a scale of 1 unit to
represent 2 km on the r-axis and 1 unit to represent 5 USD on the y-axis.
(b) Use your graphic display calculator to find
(i) ī, the mean of the lengths;
(ii) j, the mean of the prices.
(c) Plot and label the point M(7, j) on your scatter diagram.
(d) Use your graphic display calculator to find
(i)
the product-moment correlation coefficient, r;
(ii) the equation of the regression line y on r.
(e) Draw the regression line y on r on your scatter diagram.
John took a Uber ride of length 22.5 km from John F. Kennedy International Airport (JFK)
to Central Park.
(f) Use the equation of the regression line to estimate the price of John's ride from JFK to
Central Park. Give your answer correct to the nearest dollar.
(g) Give a reason why it is valid to use your regression line to estimate the price of John's
ride.
The actual cost of John's Uber rise was 40 USD.
(h) Using your answer to part (f), calculate the percentage error in the estimated price
of John's ride.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F030d8694-e671-4891-97d5-565c06affd6c%2F8fcce3de-a0c6-41e3-95a0-f547091d7a2b%2Fsympbgen_processed.jpeg&w=3840&q=75)
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