Question

A sample of 𝑛=20

n

=

20

 observations is drawn from a normal population with 𝜇=950

μ

=

950

 and 𝜎=250

σ

=

250

. Find each of the following:

A. 𝑃(𝑋

¯

>1061)

P

(

X

¯

>

1061

)

Probability = 

B. 𝑃(𝑋

¯

<838)

P

(

X

¯

<

838

)

Probability = 

C. 𝑃(𝑋

¯

>894)

P

(

X

¯

>

894

)

Probability = 

Answer 1

A.

$$P(X>1061)=1-P(X\leq1061)$$

$$=1-P(Z\leq\dfrac{1061-950}{250/\sqrt{20}})\approx1-P(Z\leq1.9856)$$

$$\approx0.023537$$

B.

$$P(X<838)=P(Z<\dfrac{838-950}{250/\sqrt{20}})$$

$$\approx P(Z<-2.0035)\approx0.022561$$

C.

$$P(X>894)=1-P(X\leq894)$$

$$=1-P(Z\leq\dfrac{894-950}{250/\sqrt{20}})\approx1-P(Z\leq-1.0018)$$

$$\approx0.841770$$