Question

1. the dotplots show the lifetimes of several brand x and brand y batteries.

a. what percentage of all the batteries (both brands) lasted more than 42 hours?
b. give a reason someone might prefer a brand x battery.
c. give a reason someone might prefer a brand y battery.

1. during the early part of a major league baseball season, many fans and players noticed that the number of home runs being hit seemed unusually large. here are the data on the number of home runs hit by american league and national league teams in the early part of that season. here are parallel boxplots and summary statistics.

summary statistics
please compare the distributions of home runs for the two leagues. describe what you see.

Explanation:

Step1: Count the number of batteries

Count the number of dots (batteries) for Brand X and Brand Y.
Brand X has \(1 + 1+1+2 + 3+3+2=13\) batteries.
Brand Y has \(1+1+1+1+4+3 + 1=12\) batteries.
Total number of batteries \(n=13 + 12=25\).

Step2: Count the number of batteries that lasted more than 42 hours

For Brand X, the number of batteries that lasted more than 42 hours: count the dots to the right of 42. There are \(2\) batteries.
For Brand Y, the number of batteries that lasted more than 42 hours: count the dots to the right of 42. There are \(3\) batteries.
Total number of batteries that lasted more than 42 hours \(m = 2+3=5\).

Step3: Calculate the percentage

The formula for percentage is \(P=\frac{m}{n}\times100\).
Substitute \(m = 5\) and \(n=25\) into the formula: \(P=\frac{5}{25}\times100 = 20\%\).

Answer:

a. \(20\%\)
b. Brand X has some batteries with relatively long - lasting times (e.g., a few batteries that last longer than most Brand Y batteries in the higher - end of the lifetime range).
c. Brand Y has a more spread - out distribution in the lower - end, which might be preferred if a wider range of lower - but - still - functional lifetimes is acceptable and there is a small number of very low - lifetime batteries that are outliers.