The heights of smart clones are distributed approximations normally with mean of 5.6 feet and standard deviation of 0.0130 feet. Let X be the night of a randomly selected clone. Find the probability that: a) x is less than 5.6186 feet b) x is greater than 5.58824 feet c) x and sits eman differ by less than 1.5 standard variations d) find c such that between 5.6-c and 5.6+c is included in 98% of the clones heights
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Find the probability that:
a) x is less than 5.6186 feet
P(X<5.6186) = P(Z< (5.6186-5.6)/.013 ) = P(Z<1.431) = .924
b) x is greater than 5.58824 feet = P(X>5.58824) = P(Z> -.90462) = .1828
c) x and sits eman differ by less than 1.5 standard variations = P(|X-x| < 1.5*Stdev) = P(-1.5<Z<1.5) = .8664
d) find c such that between 5.6-c and 5.6+c is included in 98% of the clones heights?
So, P(X< 5.6-c) = .01 ( 100-98%)/2 = 1%)
So, ((5.6-c) - 5.6)/.013 = -2.33
c = .03024
So, value of c is .03024
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