Question

V 7.2 Due in 5 hours, 3 minutes. Due Thu 07/30/2020 11:59 pm al Points Possible: 2 estions Question 1 (0/1) Question 2 (0.771) de: 0.7/2 The average time to run the SK fun run is 24 minutes and the standard deviation is 2.7 minutes. 43 runners are randomly selected to run the SK fun run. Round all answers to 4 decimal places where possible and assume a normal distribution a. What is the distribution of X? X-NI b. What is the distribution of a? - NC c. What is the distribution of * --NG d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.8824 and 24.3824 minutes. e. For the 43 runners, find the probability that their average time is between 23.8824 and 24.3824 minutes. Tint Version 1. Find the probability that the randomly selected 43 person team will have a total time less than 1010.5. For parte) and t), is the assumption of normal necessary? No Yes h. The top 10% of all 43 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes Same Helnful Videns.

Answer 1

for normal distribution z score =(X-μ)/σx
mean μ=	24
standard deviation σ=	2.7

a_)

X ~N(24 , 2.7)

b)

std error=σx̅=σ/√n=

0.4117

xbar ~ N(24 , 0.4117)

c)

Σx ~ N(1032 ,17.7051)

d)

probability =P(23.8824<X<24.3824)=P((23.8824-24)/2.7)<Z<(24.3824-24)/2.7)=P(-0.04<Z<0.14)=0.5563-0.4826=0.0737

e)

probability =P(23.8824<X<24.3824)=P((23.8824-24)/0.412)<Z<(24.3824-24)/0.412)=P(-0.29<Z<0.93)=0.8235-0.3876=0.4359

f)

probability =P(X<1010.5)=(Z<(1010.5-1032)/17.705)=P(Z<(-1.2143)=0.1123

g)

No

h)

for 10th percentile critical value of z=-1.2816

therefore corresponding value=mean+z*std deviation=1009.3100