P(X < A) = P(Z < (A - mean)/standard deviation)
a) Let the standard deviation be
P(X < 15) = 0.95
P(Z < (15 - 14)/) = 0.95
From standard normal distribution table, take the value of Z corresponding to 0.95
(14 - 13)/ = 1.96
= 0.5102
b) P(X > 15) = 1 - P(Z < 15)
= 1 - P(Z < (15 - 14)/0.83)
= 1 - P(Z < 1.20)
= 1 - 0.8849
= 0.1151
P(exactly 4 of those shoes weigh more than 0.1151)
= 8C4 x 0.11514 x 0.88494
= 0.0075
Problem #6: The weight of a sophisticated running shoe is normally distributed with a mean of...
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