3. Suppose that the amount of liquid in a bottle is normally distributed with a mean...
3. Suppose that the amount of liquid in a bottle is normally distributed with a mean of 16 oz and a standard deviation of 0.2 oz. If we take a random sample of 10 bottles from a production run, what is the probability that the sample mean is between 15.99 and 16.01?
Homework Answers
Solution :
Given that,
mean = 
= 16
standard deviation = 
= 0.2
=
/ 
n = 0.2 /
10 = 0.0632
= P[(15.99 - 16) / 0.0632< (
-
)
/
< (16.01 - 16) / 0.0632)]
= P(-0.16 < Z < 0.16)
= P(Z < 0.16) - P(Z < -0.16)
= 0.5636 - 0.4364
= 0.1272
Probability = 0.1272
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