Question
In: Statistics and Probability
A sample of n=23 observations is drawn from a normal population with μ=1030 and σ=210. Find...
A sample of n=23 observations is drawn from a normal population with μ=1030 and σ=210. Find each of the following:
A. P(X¯>1117)
Probability =
B. P(X¯<964)
Probability =
C. P(X¯>1012)
Probability =
Solutions
Expert Solution
Solution :
Given that ,
mean = 
= 1030
standard deviation = 
= 210
=
/ 
n = 210 /
23 = 43.7880
A.
P(
> 1117) = 1 - P(
< 1117)
= 1 - P[(
- 
) /
< (1117 - 1030) / 43.7880]
= 1 - P(z < 1.99)
= 1 - 0.9767
= 0.0233
Probability = 0.0233
B.
P(x 
964)
= P[(x -
) /
(964 - 1030) / 43.7880]
= P(z
-1.51)
= 0.0655
Probability = 0.0655
C.
P(
> 1012) = 1 - P(
< 1012)
= 1 - P[(
-
) /
< (1012 - 1030) / 43.7880]
= 1 - P(z < -0.41)
= 1 - 0.3409
= 0.6591
Probability = 0.6591
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