Yuki and Zana are on a swimming team. They often compete against each other in the 100 meter freestyle race.

Yuki and Zana are on a swimming team. They often compete against each other in the 100 meter freestyle race. Yuki's times in this race are normally distributed with a mean of 80 seconds and a standard deviation of 4.2 seconds. Zana's times are also normally distributed with a mean of 85 seconds and a standard deviation of 5.6 seconds. We can assume that their times are independent. Suppose we choose a random 100 meter freestyle race and calculate the difference between their times.

The difference between the two means, which is

85 - 80 = 5

Step 2: Next add the squares of the given standard deviations.

`(4.2)^2` + `(5.6)^2` = 49

Step 3: Find the square root of this to get the variance as

`\sqrt{49}` =7

P( Yuki is faster) = 0.76 (After rounding off to the first two decimals)