Stats question

Question

Water bottles labeled 1.5 liter contain actual water amounts that are approximately Normally distributed with a mean of 1.55 liter and a standard deviation of 0.1 liter. Someone buys 4 water bottles. What is the probability that the average amount of water per water bottle would be less than 1.5 liter? Show what you typed in your calculator. using the ti-84 you enter normalcdf(-99,1.5,1.55, .1/2) = .1585. I don't understand where they got the .1/2 from. Please help :)

Answer 1

Hi Daniel, 

When you write down the important variables given correctly, then it is possible to get the correct answer when using your calculator. Here is how the normal cumulative distribution function in your calculator works. Get

Actual amount = X = 1.5

The mean = μ = 1.55 liters

Standard deviation is = σ = 0.1

Find probability that X < 1.5

P(X < 1.5) = normalcdf(-99, X,  μ, σ/2)    [ -99 is the tolerance of the intrument] Plug in the numbers above

                = normalcdf(-99, 1.5, 1.55, 0.1/2) or 

P(X < 1.5)= normalcdf(-99, 1.5, 1.55, 0.05) 

               = 0.1586