"The lifetime of a particular type of TV follows a normal distribution with =4800 hours, and = =400 hours.

(a) Find the probability that a single randomly-chosen TV will last less than 4,500 hours. Use R to assist with your computations.

(b) Find the probability that the mean lifetime of a random sample of 16 TVs is less than 4,500 hours. Use R to assist with your computations."

Ok, firstly, does the first line say that the lifetime of a particular type of TV follows a normal distribution, then does that mean it is the

**population**they are talking about with a mean =4800 hours, and standard deviation =400?

Assuming the first part is the

**population**mean and standard deviation, then I can work out the probability of a single randomly-chosen TV lasting less than 4500 hours, yet I am not confident it is the population.

Question a)

SE = standard_deviation/sqrt(1)

Z = (4500-4800)/SE

pnorm(Z) = 0.23

Question b) using central limit theorem

SE = standard_deviation/sqrt(16)

Z = (4500 – 4800)/SE

Pnorm(Z) = 0.001349898

Now I can not see how 16 TV's has such a small probability of being less than 4500hours when 1 TV has a probability of 23%.

Can someone please help me understand this.