Fill in the following blanks by stating the properties of real numbers used. (i) − ( + )
(ii) − −
(iii) − −
(iv) −
(v) −5y

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.1. (round your answers to four decimal places.) (a) if the distribution is normal, what is the probability that the sample mean hardness for a random sample of 8 pins is at least 51?