Question

Diagrams of the normal distribution are almost mandatory

Suppose that battery lives are normally distributed with a mean of 12.85 hours and a standard deviation of 1.93 hours. What is the minimum sample size that would be required so that the probability of obtaining a sample mean above 13.5 hours is less than 1%?

Answer 1

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R Script:

n<-rnorm(10000,12.85,1.93) #generating random number from given normal population
plot(density(n), main="Population density curve: N(mean=12.85,st dv= 1.93)")# density curve for the given normal population
Z0.01<-qnorm(0.01,0,1,lower.tail = F);Z0.01 #critical value for 1% probability
stN<-rnorm(10000,0,1) #generating random numbers from Standard normal populations
plot(density(stN), main="N(mean=0,st dv=1)")# density curve for the standard normal population

Density curve plots:

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