16)
Solution :
Given that ,
mean = = 400
standard deviation = = 10
(a)
P(400 < x < 415) = P((400 - 400 / 10) < (x - ) / < (415 - 400) / 10) )
= P(0 < z < 1.5)
= P(z < 1.5) - P(z < 0)
= 0.9332 - 0.5 = 0.4332
Probability = 0.4332
(b)
P(395 < x < 400) = P((395 - 400 / 10) < (x - ) / < (400 - 400) / 10) )
= P(-0.5 < z < 0)
= P(z < 0) - P(z < -0.5)
= 0.5 - 0.3085 = 0.1915
Probability = 0.1915
(c)
P(x < 395) = P((x - ) / < (395 - 400) / 10) = P(z < -0.5)
Using standard normal table,
P(x < 395) = 0.3085
Probability = 0.3085
16. The mean of a normal probability distribution is 400 pounds. The standard deviation is 10...
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