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2. May is interested in purchasing the local hardware store in her home- town. After examining the store accounts for the past two years, she found that the store had been earning a gross amount of over $850 per day for 70% of the business days it was open. A random sample of n = 20 business days is selected from the last two years. Let X represent the number of days where the store earned over $850 gross. (a) notation. Justify your choice of distribution. Write down the probability distribution of X using the 'X ~ (b) the probability that in the sample the store will gross over $850 for the following numbers of days. If you wish, you can use notation such as P(X < ...) to write your answers e.g. for 2(b)i you can write P(X = 10) = .. Using Excel and providing the exact Excel functions you use, give i. exactly 10 business days ii. at least 10 business days iii. between 6 and 16 (inclusive) business days iv. fewer than 6 business days. (c) period of three months from the date of purchase. She then takes a random sample of 20 business days from those three months and finds that the store did gross over $850 per day for fewer than 6 business days in her sample. Do you think this should this make May suspect that p (the probability of grossing over $850 on a business day) is now less than 0.7? Explain your answer. May decides to purchase the store and records the accounts for a (d) i. If the value of p was 0.6, calculate P(X < 6) for a sample of n = 20. ii. Suggest a value of p that might mean that May would not have been surprised to find the store grossed over $850 for fewer than 6 business days, briefly explaining your answer.

2. May is interested in purchasing the local hardware store in her home- town. After examining the store accounts for the past two years, she found that the store had been earning a gross amount of over $850 per day for 70% of the business days it was open. A random sample of n = 20 business days is selected from the last two years. Let X represent the number of days where the store earned over $850 gross. (a) notation. Justify your choice of distribution. Write down the probability distribution of X using the 'X ~ (b) the probability that in the sample the store will gross over $850 for the following numbers of days. If you wish, you can use notation such as P(X < ...) to write your answers e.g. for 2(b)i you can write P(X = 10) = .. Using Excel and providing the exact Excel functions you use, give i. exactly 10 business days ii. at least 10 business days iii. between 6 and 16 (inclusive) business days iv. fewer than 6 business days. (c) period of three months from the date of purchase. She then takes a random sample of 20 business days from those three months and finds that the store did gross over $850 per day for fewer than 6 business days in her sample. Do you think this should this make May suspect that p (the probability of grossing over $850 on a business day) is now less than 0.7? Explain your answer. May decides to purchase the store and records the accounts for a (d) i. If the value of p was 0.6, calculate P(X < 6) for a sample of n = 20. ii. Suggest a value of p that might mean that May would not have been surprised to find the store grossed over $850 for fewer than 6 business days, briefly explaining your answer.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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2. May is interested in purchasing the local hardware store in her home- town. After examining the store accounts for the past two years, she found that the store had been earning a gross amount of over $850 per day for 70% of the business days it was open. A random sample of n = 20 business days is selected from the last two years. Let X represent the number of days where the store earned over $850 gross. Write down the probability distribution of X using the 'X ~ (a) notation. Justify your choice of distribution. (b) the probability that in the sample the store will gross over $850 for the following numbers of days. If you wish, you can use notation such as P(X < ...) to write your answers e.g. for 2(b)i you can write P(X = 10) = .. Using Excel and providing the exact Excel functions you use, give i. exactly 10 business days ii. at least 10 business days iii. between 6 and 16 (inclusive) business days iv. fewer than 6 business days. (c) period of three months from the date of purchase. She then takes a random sample of 20 business days from those three months and finds that the store did gross over $850 per day for fewer than 6 business days in her sample. Do you think this should this make May suspect that p (the probability of grossing over $850 on a business day) is now less than 0.7? Explain your answer. May decides to purchase the store and records the accounts for a (d) i. If the value of p was 0.6, calculate P(X < 6) for a sample of n = 20. ii. Suggest a value of p that might mean that May would not have been surprised to find the store grossed over $850 for fewer than 6 business days, briefly explaining your answer.
Transcribed Image Text:2. May is interested in purchasing the local hardware store in her home- town. After examining the store accounts for the past two years, she found that the store had been earning a gross amount of over $850 per day for 70% of the business days it was open. A random sample of n = 20 business days is selected from the last two years. Let X represent the number of days where the store earned over $850 gross. Write down the probability distribution of X using the 'X ~ (a) notation. Justify your choice of distribution. (b) the probability that in the sample the store will gross over $850 for the following numbers of days. If you wish, you can use notation such as P(X < ...) to write your answers e.g. for 2(b)i you can write P(X = 10) = .. Using Excel and providing the exact Excel functions you use, give i. exactly 10 business days ii. at least 10 business days iii. between 6 and 16 (inclusive) business days iv. fewer than 6 business days. (c) period of three months from the date of purchase. She then takes a random sample of 20 business days from those three months and finds that the store did gross over $850 per day for fewer than 6 business days in her sample. Do you think this should this make May suspect that p (the probability of grossing over $850 on a business day) is now less than 0.7? Explain your answer. May decides to purchase the store and records the accounts for a (d) i. If the value of p was 0.6, calculate P(X < 6) for a sample of n = 20. ii. Suggest a value of p that might mean that May would not have been surprised to find the store grossed over $850 for fewer than 6 business days, briefly explaining your answer.
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