Question
In: Statistics and Probability
Given a population with a mean of µ = 100 and a variance σ2 = 14,...
Given a population with a mean of µ = 100 and a variance σ2 = 14, assume the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 46 is obtained. What is the probability that 98.80 < x¯ < 100.92?
Solutions
Expert Solution
Solution :
Given that,
mean = 
= 100
standard deviation = 
= 3.7417
n = 46
=
= 100
=
/ 
n = 3.7417/
46 = 0.5517
P( 98.80 < 
< 100.92) = P((98.80 - 100) / 0.5517<(
-
)
/
< (100.92 - 100) / 0.5517))
= P(-2.18 < Z < 1.67)
= P(Z < 1.67) - P(Z < -2.18) Using standard normal table,
= 0.9525 - 0.0146
= 0.9379
Probability = 0.9379
orchestra answered 3 years agoRelated Solutions
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