Question

The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6.0 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.72 ounces and a standard deviation of 0.11 ounces. What percentage of the pucks produced at this factory cannot be used by the National Hockey League?

Round your answer to two decimal places.

The percentage of pucks that cannot be used is

Answer 1

Solution :

Given that ,

mean = $\mu$ = 5.72

standard deviation = $\sigma$ = 0.11

P(5.5< x < 6.0) = P[(5.5 - 5.72) / 0.11< (x - $\mu$ ) / $\sigma$ _{$\bar x$} < (6.0 - 5.72) / 0.11)]

= P(-2 < Z <2.55 )

= P(Z <2.55 ) - P(Z <-2 )

Using z table,  

=   0.9946 - 0.0228

=0.9718

=97.18%