e average amount of money spent for lunch per person in the college cafeteria is $6 and the standard viation is $2.51. Suppose that 13 randomly selected lunch patrons are observed. Assume the distributi money spent is normal, and round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. What is the distribution of ? a N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.4459 and $5.844. d. For the group of 13 patrons, find the probability that the average lunch cost is between $5.4459 a $5.844. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes nt: ome Helpful Videos: Finding the Sampling Distribution [+] • Finding a Probability Using the Central Limit Theorem [+] Finding Value Given a Probability Using the Central Limit Theorem [+] • The Central Limit Theorem For Sums [+] lint

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The average amount of money spent for lunch per person in the college cafeteria is $6 and the standard
deviation is $2.51. Suppose that 13 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. What is the distribution of X? X NG
b. What is the distribution of ? a N(
c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is
between $5.4459 and $5.844.
d. For the group of 13 patrons, find the probability that the average lunch cost is between $5.4459 and
$5.844.
e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes
Hint:
Some Helpful Videos:
Finding the Sampling Distribution [+]
• Finding a Probability Using the Central Limit Theorem
Finding Value Given a Probability Using the Central Limit Theorem [+]
• The Central Limit Theorem For Sums 2 [+]
[+]
Hint
Transcribed Image Text:The average amount of money spent for lunch per person in the college cafeteria is $6 and the standard deviation is $2.51. Suppose that 13 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. What is the distribution of X? X NG b. What is the distribution of ? a N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.4459 and $5.844. d. For the group of 13 patrons, find the probability that the average lunch cost is between $5.4459 and $5.844. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes Hint: Some Helpful Videos: Finding the Sampling Distribution [+] • Finding a Probability Using the Central Limit Theorem Finding Value Given a Probability Using the Central Limit Theorem [+] • The Central Limit Theorem For Sums 2 [+] [+] Hint
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