A population has a mean of 15 and a standard deviation of 3. What is the...
A population has a mean of 15 and a standard deviation of 3. What is the probability that a sample of 4 individuals will have a mean between 16.5 and 18? (2 marks)
Homework Answers
Solution :
Given that,
mean = 
= 15
standard deviation = 
= 3
=
/ 
n = 3 /
4 = 1.5
= P[(16.5 - 15) /1.5 < (
-
)
/
< (18 - 15) /1.5 )]
= P(1 < Z < 2)
= P(Z < 2) - P(Z < 1)
= 0.9772 - 0.8413
= 0.1359
Probability = 0.1359
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