The average amount of money spent for lunch per person in the college cafeteria is $7.42 and the standard deviation is $2.58. Suppose that 8 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

 

A) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $8.4717 and $9.0778. ____

 

B) For the group of 8 patrons, find the probability that the average lunch cost is between $8.4717 and $9.0778. ____

in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Z₁=(8.4717-7.42)/2.58=0.4076, Z₂=(9.0778-7.42)/2.58=0.6426.

(A) p(Z₁)=0.6582, p(Z₂)=0.7397, so the probability for the defined range is the difference between these probabilities: 0.0815 approx. This applies to one individual.

(B) In the sample group of 8, the number of degrees of freedom is 7. The SD needs to be adjusted for the sample: 2.58/√8=0.9122 and we use the t test.

t₁=(8.4717-7.42)/0.9122=1.1530, t₂=(9.0778-7.42)/0.9122=1.8174.

From t tables with dof=7, p(t₁)=0.1443, p(t₂)=0.0419, and the difference is 0.1024 approx. This is slightly higher than the probability for one individual.

by Top Rated User (782k points)

Related questions

1 answer
asked Oct 14, 2019 in Statistics Answers by anonymous | 606 views
1 answer
asked May 13, 2019 in Statistics Answers by anonymous | 67 views
1 answer
asked Feb 17, 2019 in Statistics Answers by anonymous | 145 views
1 answer
asked Nov 19, 2018 in Statistics Answers by anonymous | 98 views
1 answer
1 answer
asked Sep 21, 2017 in Statistics Answers by Stephon | 131 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,304 questions
90,731 answers
2,173 comments
101,445 users