Solution: Given that mean = 2800, sd = 860
a. P(X < 2000) = P((X-mean)/sd < (2000-2800)/860)
= P(Z < -0.9302)
= 1 - P(Z < 0.9302)
= 1 - 0.8238
= 0.1762
b. P(1500 < X < 2500) = P((1500-2800)/860 < Z <
(2500-2800)/860 )
= P(-1.5116 < Z < -0.3488)
= P(Z < -0.3488) - P(Z < -1.5116)
= 0.3632 - 0.0655
= 0.2977
c. P(X > 3000) = P(Z > (3000-2800)/860)
= P(Z > 0.2326)
= 0.4090
d. P(X > x) = 0.01, for Z = 2.326
X = mean + Z*sd = 2800 + (2.326*860) = 4800.36 = 4801(rounded)
Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence...
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