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The number of fan letters received by a band each month is distributed normally, with a mean of 6.5 and a standard deviation of 2.5. Use the Z calculator to answer the questions below: 6a) Use continuity correction to determine the probability that the band receives no more than 5 fan letters in a given month. Round to the nearest 0.1%. 6b) Calculate the probability that the average number of fan letters per month which the band receives over a 10-month period at least 7. Round to the nearest 0.1%. MM

The number of fan letters received by a band each month is distributed normally, with a mean of 6.5 and a standard deviation of 2.5. Use the Z calculator to answer the questions below: 6a) Use continuity correction to determine the probability that the band receives no more than 5 fan letters in a given month. Round to the nearest 0.1%. 6b) Calculate the probability that the average number of fan letters per month which the band receives over a 10-month period at least 7. Round to the nearest 0.1%. MM

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I need help with 6a and 6b, thank you!

**Problem 6: Fan Letters Received by a Band** The number of fan letters received by a band each month is distributed normally, with a mean of 6.5 and a standard deviation of 2.5. Use the Z calculator to answer the questions below: **6a.** Use continuity correction to determine the probability that the band receives no more than 5 fan letters in a given month. Round to the nearest 0.1%. **6b.** Calculate the probability that the average number of fan letters per month which the band receives over a 10-month period is at least 7. Round to the nearest 0.1%. --- **Problem 7: Fruit Stand Profit Maximization** You have a fruit stand. At the beginning of each week, you order some fruit, and sell it retail at a 100% markup. For example, a piece of fruit that you sell retail for $5 cost you $2.50. At the end of the week, any fruit not sold is sold to a juicer for 40% of what you paid for it (or 20% of the retail price). (For example, you pay $2.50 for a piece of fruit, which you can sell retail for $5, but if you don’t sell it retail, you can sell it to a juicer for $1.) The average amount of fruit that your customers want to purchase that week is $10,000 (Retail. In other words, you paid $5,000 for it). This amount is distributed normally, with a standard deviation of $1,000. To maximize your long-term profits, how much fruit (in terms of retail price) should you purchase each week? Round, if necessary, to the nearest $10. --- **Problem 8: Auditioning Lead Guitarists** You are auditioning lead guitarists, in random order, for a project band. 35 people have signed up to audition, of which you will consider exactly 5 to be a good fit. What is the probability that you find the first person who auditions to be a good fit, then none of the next six people to be a good fit? Round to the nearest 0.1%.
Transcribed Image Text:**Problem 6: Fan Letters Received by a Band** The number of fan letters received by a band each month is distributed normally, with a mean of 6.5 and a standard deviation of 2.5. Use the Z calculator to answer the questions below: **6a.** Use continuity correction to determine the probability that the band receives no more than 5 fan letters in a given month. Round to the nearest 0.1%. **6b.** Calculate the probability that the average number of fan letters per month which the band receives over a 10-month period is at least 7. Round to the nearest 0.1%. --- **Problem 7: Fruit Stand Profit Maximization** You have a fruit stand. At the beginning of each week, you order some fruit, and sell it retail at a 100% markup. For example, a piece of fruit that you sell retail for $5 cost you $2.50. At the end of the week, any fruit not sold is sold to a juicer for 40% of what you paid for it (or 20% of the retail price). (For example, you pay $2.50 for a piece of fruit, which you can sell retail for $5, but if you don’t sell it retail, you can sell it to a juicer for $1.) The average amount of fruit that your customers want to purchase that week is $10,000 (Retail. In other words, you paid $5,000 for it). This amount is distributed normally, with a standard deviation of $1,000. To maximize your long-term profits, how much fruit (in terms of retail price) should you purchase each week? Round, if necessary, to the nearest $10. --- **Problem 8: Auditioning Lead Guitarists** You are auditioning lead guitarists, in random order, for a project band. 35 people have signed up to audition, of which you will consider exactly 5 to be a good fit. What is the probability that you find the first person who auditions to be a good fit, then none of the next six people to be a good fit? Round to the nearest 0.1%.
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