Question

The mean weight of loads of rock is 47.0 tons with a standard deviation of 8.0 tons. If 24 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 46.5 tons. Assume that the variable is normally distributed. In addition to the answer, please write out your steps and thoughts that led you to your answer.

Answer 1

Solution :

Given that,

mean = = 47

standard deviation = = 8

n = 24

= 47

=  / n = 8 / 24=1.63

P( <46.5 ) = P[( - ) / < (46.5 - 47) /1.63 ]

= P(z <-0.31 )

Using z table  

= 0.3783   

probability= 0.3783