for 3-(b), why we can calculate probability since our random sample is 4 (<30)?
ID: 3371260 • Letter: F
Question
for 3-(b), why we can calculate probability since our random sample is 4 (<30)?
3. The weights of adobe bricks used for construction follow a normal distribution with mean 5.0 pounds and standard deviation 0.2 pounds. (a) Only 12% of bricks are heavier than what weight? (b) We take a random sample of four bricks. Can you calculate the probability that the average weight of these four bricks is greater than 5.1 pounds? If so, calculate the probability. If not, explain why not. (c) What is the probability that the total weight of a random sample of 50 bricks is less than 248 pounds? (d) Is the probability you calculated in (c) exact or approximate? Explain.Explanation / Answer
a) for top 12 % ; crtiical z =1.17
hence corresponding weight =mean +z*std deviation =5+1.17*0.2=5.234 poounds
b)
as we have given that our parent population distribution is normal ; therefore it has been warranted that sample distribution of all sample size should be normal and therefore we can use normal distribution to calculate probability,
P(Xbar>5.1)=P(Z>(5.1-5)/(0.2/sqrt(4))=P(Z>1)=0.1587
c)
here P(Xbar<248/50)=P(Xbar<4.96)=P(Z<(4.96-5)/(0.2/sqrt(50))=P(Z<-1.41)=0.0793
d)
this would be exact as we know that distribution is normal cause parent distribution is normal
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