How do I find the total SD?
$\displaystyle
Mean= 4.9 4.7 4.5 4.8
SD= .15 .16 .14 .15
$
There are 4 numbers for each.
There are 4 runners on a team. Each runner runs a mile. The team time is the sum of the individual times.
Runner 1 4.9 .15
Runner 2 4.7 .16
Runner 3 4.5 .14
Runner 4 4.8 .15
the 1st number is the mean (minutes), and the second is the sd.
a) Runner 3 thinks that he can run a mile in less than 4.2 minutes in the next race. Is it likely to happen?
b) What is the SD of the distribution?
With only one race, there is NO Standard Deviation. The question is bad.
If it is intended to be a season's collected data, that's a different story. Just calculate the number of standard deviations required to beat 4.20.
(4.2-4.9)/0.15 = -4.6666 standard deviations. Pretty low probability, eh?
a) Can't be done unless an assumption on the distribution is made. If you assume that Runner 3's times follow a normal distribution with mean 4.5 and sd 0.14, then calculate Pr(X < 4.2).
b) The variance of a sum of uncorrelated random variables is given by
$\displaystyle \sigma_1^2 + \sigma_2^2 + \sigma_3^2 + ........$