219k views
2 votes
A bottling plant produces 1 liter bottles of soda. The actual distribution of volumes of soda dispensed to bottles is Normal, with mean μ and standard deviation σ = 0.05 liter. We randomly select 6 bottles andmeasure the volume of soda in each. The results of these 6 measurements (all in liter units) are 1.05 1.04 1.01 1.06 0.94 0.99. Based on these data, a 90% confidence interval for μ is

User Mysterio
by
8.3k points

1 Answer

6 votes

Given:

Standard deviation = 0.05

Mean = (1.05 + 1.04 + 1.01 + 1.06 + 0.94 + 0.99 / 6) = 1.015

n = 6

Confidence level = 90%

Z score for 90% = 1.645

Solution:

Formula is mean ± z (s / sqrt (n))

= 1.015 ± (1.645) (0.05/ sqrt (6)

= 1.015 ± (1.645) (0.020412414)

= 1.015 ± 0.033578421

= 0.9814 < x < 1.0486 is the confidence interval

User Bayrinat
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories