Question

In: Statistics and Probability

Let X be N(µ = 16, σ^2 = 4). Graph its p.d.f. and compute the following...

Let X be N(µ = 16, σ^2 = 4). Graph its p.d.f. and compute the following quantities.

(a) Compute the probability P(X > 10).

(b) Compute the probability P(|X − 16| < 2).

(c) Compute c so that P(X ≤ c) = 0.95.

Expert Solution

a)

= P(Z > -3)

= 1 - P(Z < -3)

= 1 - 0.0013

= 0.9987

b)

= P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

c)

or, c = 16 + 1.645 * 2

or, c = 19.29

orchestra answered 2 years ago

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