Question

the following data are the numbers of miles of bike lanes per square mile for a sample of 10 of the top 25 cities with the most miles of bike lanes. complete parts (a) through (e).
miles of bike lanes
1 5
2 6 7 8 9
3 0 7 7
4 3
a. construct a stemplot.
b. how many of the 10 cities have at most 3.0 miles of bike lanes per square mile?
of the 10 cities, 7 have at most 3.0 miles of bike lanes per square mile. (type a whole number.)
c. find the proportion of the 10 cities that have at least 3.7 miles of bike lanes per square mile.
of the 10 cities, 0.3 have at least 3.7 miles of bike lanes per square mile. (round to one decimal place as needed.)
d. find the 80th percentile of the 10 observations.
the 80th percentile of the 10 observations is 3.7 miles of bike lanes per square mile. (type an integer or a decimal. do not round.)
e. philadelphia has more miles of bike lanes per square mile than any other of these 10 cities. at least how many miles of bike lanes per square mile is that?
philadelphia has at least □ miles of bike lanes per square mile. (type an integer or a decimal. do not round.)

Explanation:

Step1: Arrange data in ascending order

1.5, 2.2, 2.6, 2.7, 2.8, 2.9, 3.0, 3.7, 3.7, 4.3

Step2: Construct stemplot

Stem | Leaf
--- | ---
1 | 5
2 | 2 6 7 8 9
3 | 0 7 7
4 | 3

Step3: Count number of cities with at most 3.0 miles

Count the values less than or equal to 3.0: 1.5, 2.2, 2.6, 2.7, 2.8, 2.9, 3.0. There are 7 cities.

Step4: Calculate proportion of cities with at least 3.7 miles

There are 3 values (3.7, 3.7, 4.3) that are at least 3.7. Proportion = $\frac{3}{10}=0.3$

Step5: Calculate 80th percentile

Index $i = 0.8\times n$, where $n = 10$. So $i=0.8\times10 = 8$. The 80th - percentile is the value at the 8th position (after arranging in ascending order). The 8th value is 3.7.

Step6: Determine value for Philadelphia

Since Philadelphia has more miles of bike - lanes per square mile than any of the other 10 cities, it has at least 4.3 miles of bike - lanes per square mile.

Answer:

a. Stem | Leaf
--- | ---
1 | 5
2 | 2 6 7 8 9
3 | 0 7 7
4 | 3
b. 7
c. 0.3
d. 3.7
e. 4.3