Question

A sample of n = 16 observations is drawn from a
normal population with μ = 1,000 and σ = 200.
Find the following.
a. P(X > 1,050)
b. P(X < 960)
c. P(X > 1,100)

Answer 1

Solution

a. P(x>1050)

$$P(X>1050) =1-P(X<1050)$$

$$=1- \phi ({x- \mu \over {\sigma \over \sqrt{n}}})$$

$$=1 - \phi ({1050-1000 \over {200 \over \sqrt{16}} })=1- \phi (1)$$ $$=1-0.8413$$ $$=0.1587$$

b. P(X<960)

$$=\phi ({960-1000 \over {200 \over \sqrt{16}}} )= \phi(-0.8)$$

$$=0. 2119$$

c. P(X>1100)

$$=1 - \phi ({1100-1000 \over {200 \over \sqrt{16}} })=1- \phi (2)$$

$$=1-0.9772$$ $$=0.0228$$