1. The time to bike from Bush Library to Zachry Building is a random variable wi
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Question
1. The time to bike from Bush Library to Zachry Building is a random variable with mean 15 minutes and standard deviation 4 minutes. If 36 students biked from Bush Library to Zachry, all at different times, what is the probability that the average time for these 36 students is greater than 15.5 minutes?
2. The mean and standard deviation of the number of calories pumped in 1 minute are 12 cals and 1 cal respectively on a rowing machine. What is the probability of pumping more than 190 calories in 15 minutes?
Explanation / Answer
mean is 15 and s is 4
for sample size of 36, the standard error SE is s/sqrt(N) = 15/SQRT(36)=2.5
z is given as (x-mean)/SE
thus P(x>15.5)=P(z>(15.5-15)/2.5)=P(z>0.2) or 1-P(z<0.2)
from normal distribution table we get 1-0.5793=0.4207
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