Question
In: Statistics and Probability
Suppose a simple random sample of size n=64 is obtained from a population with μ=76 and...
Suppose a simple random sample of size n=64 is obtained from a population with μ=76 and σ=8.
(a) Describe the sampling distribution of x̅
(b) What is P (x̅ > 77.7)?
(c) What is P (x̅ ≤ 73.65)?
(d) What is P (74.5 < x̅ < 78.15)?
Solutions
Expert Solution
Solution :
(a)
= 76
=
/ 
n = 8 /
64 = 1
(b)
P(
> 77.7) = 1 - P(
< 77.7)
= 1 - P[(
-
) /
< (77.7 - 76) / 1]
= 1 - P(z < 1.7)
= 0.0446
(c)
P(
73.65) = P((
-
) /
(73.65 - 76) / 1)
= P(z -3.35)
= 0.0004
(d)
= P[(74.5 - 76) / 1 < (
-
)
/
< (78.15 - 76) / 1)]
= P(-1.5 < Z < 2.15)
= P(Z < 2.15) - P(Z < -1.5)
= 0.9842 - 0.0668
= 0.9174
orchestra answered 1 year agoRelated Solutions
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