A road bike frame is advertised to weigh no more than 900g. The actual frame weight distribution is normal with standard deviation of 20g. What should the mean weight be so that the advertisement claim is true for al least 99% of all frames?
Solution:-
Given that,
x = 900 g
standard deviation = = 20 g
Using standard normal table,
P(Z < z) = 99%
= P(Z < z ) = 0.99
= P(Z < 2.33 ) = 0.99
z = 2.33
Using z-score formula,
x = z * +
900 = 2.33 * 20 +
= 900 - ( 2.33 * 20 )
= 853.4
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