Question

Assume that a standard dumptruck owned by a highway department can transport 1.4 tons of dirt per load (assume this is a population mean), with a population standard deviation of 0.28 tons. Suppose the highway department is concerned about some of their trucks not being able to haul as much as most, and in a sample of six trucks, they hauled an average of 1.11 tons of dirt. Assuming that the population is normally distributed, what is the probability that a sample of six trucks will on average haul less than 1.11 tons of dirt per load?

Answer 1

Solution :

= / n = 0.28 / 6

P( < 1.11) = P(( - ) / < (1.11 - 1.4) / 0.28 / 6 )

= P(z < -2.54)

= 0.0055

Probability = 0.0055