18.4 a) The Central High School team is very confident that they will beat their rivals from South High School. In act, he Central team agrees to add 1 minute to their total time to make the competition more fair. What is the mean and standard deviation of the distribution of team times for Central High School, after adding the I minute?

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nunners in similar races are approximately normally distributed with the following means and standard
(a) Runner 3 thinks that he can run a mile in less than 4.2 minutes in the next race. Is this likely to happen?
12. The Central High School relay team includes 4 runners. The team in planning to participate in a race in
which each runner runs a mile. The team time is the sum of the individual times for the 4 runners. Assume that
the individual times for the 4 runners are all independent of each other. The individual times, in minutes, of the
deviations.
Mean Standard Deviation
0.15
Runner 1
4.9
Runner 2
4.7
0.16
Runner 3
4.5
0.14
Runner 4
4.8
0.15
Explain.
P(xcui2)= P(22-2:143) = 0.16
Z= 4.2-4.5
.14
= -2.143d
unlikely because it's only 1.6%.of the tmme
) The distribution of possible team times is approximately normal. What are the mean and standard deviation
fthis distribution?
Hx = 4.9+4.7+ 4.5+4.8=18.9 min
Ox = J.15+16?+ ,14?+,15?
Jo902
Ox =,3003 mun
:) Suppose that the team's best time to date is 18.4 minutes. What is the probability that the team will beat its
own best time in the next race?
P(xi+ Yz+Xz+ Xu < 184) = P(Z <- lo65)= 0.48
2=18.4-18.9= -1i665
%3D
3003
ditum
18.4
18.9
ta) The Central High School team is very confident that they will beat their rivals from South High School. In
tact, the Central team agrees to add 1 minute to their total time to make the competition more fair. What is the
mean and standard deviation of the distribution of team times for Central High School, after adding the I
minute?
Transcribed Image Text:nunners in similar races are approximately normally distributed with the following means and standard (a) Runner 3 thinks that he can run a mile in less than 4.2 minutes in the next race. Is this likely to happen? 12. The Central High School relay team includes 4 runners. The team in planning to participate in a race in which each runner runs a mile. The team time is the sum of the individual times for the 4 runners. Assume that the individual times for the 4 runners are all independent of each other. The individual times, in minutes, of the deviations. Mean Standard Deviation 0.15 Runner 1 4.9 Runner 2 4.7 0.16 Runner 3 4.5 0.14 Runner 4 4.8 0.15 Explain. P(xcui2)= P(22-2:143) = 0.16 Z= 4.2-4.5 .14 = -2.143d unlikely because it's only 1.6%.of the tmme ) The distribution of possible team times is approximately normal. What are the mean and standard deviation fthis distribution? Hx = 4.9+4.7+ 4.5+4.8=18.9 min Ox = J.15+16?+ ,14?+,15? Jo902 Ox =,3003 mun :) Suppose that the team's best time to date is 18.4 minutes. What is the probability that the team will beat its own best time in the next race? P(xi+ Yz+Xz+ Xu < 184) = P(Z <- lo65)= 0.48 2=18.4-18.9= -1i665 %3D 3003 ditum 18.4 18.9 ta) The Central High School team is very confident that they will beat their rivals from South High School. In tact, the Central team agrees to add 1 minute to their total time to make the competition more fair. What is the mean and standard deviation of the distribution of team times for Central High School, after adding the I minute?
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