Question

# The heights of smart clones are distributed approximations normally with mean of 5.6 feet and standard...

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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