Chapter 06, Section 6.3, Problem 035 The pucks used by the National Hockey Leagu

Question

Chapter 06, Section 6.3, Problem 035 The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 60 ounces Supgose the weights of cks prouced at a factory are rormally distrbuited wth a mean of 5.78 unces and a standard deviation of 0.13 ounces. What percentage of the pucks preduced at this factory ct b usd by the National Hockey Leagen Round your answer to two decimal places. The percentage of pucks that cannot be used is Click if you would like to Show Work for this question: Open Show Wonk

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 5.78
standard Deviation ( sd )= 0.13

To find P(a < = Z < = b) = F(b) - F(a)
P(X < 5.5) = (5.5-5.78)/0.13
= -0.28/0.13 = -2.1538
= P ( Z <-2.1538) From Standard Normal Table
= 0.0156
P(X < 6) = (6-5.78)/0.13
= 0.22/0.13 = 1.6923
= P ( Z <1.6923) From Standard Normal Table
= 0.9547
P(5.5 < X < 6) = 0.9547-0.0156 = 0.9391

percentage of pucks that can not be used as = 1- 0.9391 = 0.0609 = 6.09%

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