Statistics Module 3

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Laurentian University *

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Feb 20, 2024

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OPER 5001EL 12 – Business Statistics (2022SP) Professor: Matthias Takouda Module 3 - Lesson 3 Weekly Assignment Due Date: June 12, 2022 Group E Group Members: Jdlddd

OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 2 of 10 1.) 7.81 The weekly demand for Baked Lay’s potato chips at a certain Subway sandwich shop is a random variable with mean 450 and standard deviation 80. Find the value(s) of X for each event. Show your work. Treating the distribution as a continuous normal distribution a. Highest 50 percent ← using standard values ← using Appendix C-2 b. Lowest 25 percent ← using standard values ← using Appendix C-2 c. Middle 80 percent Need to find values for 10% to 90% ← using standard values ← using standard values ← appendix C-2 ← appendix C-2 ← standardizing transfomation ← standardizing transfomation

OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 3 of 10 d. 5th percentile ← using standard values ← using Appendix C-2 ← standardizing transfomation

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OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 4 of 10 2.) 7.83 The amounts spent by customers at a Noodles & Company restaurant during lunch are normally distributed with a mean equal to $7.00 and a standard deviation equal to $0.35. Treating the distribution as a continuous normal distribution a. What amount is the first quartile? ← using standard values ← using Appendix C-2 ← standardizing transfomation First quartile is $6.77 b. The second quartile? This is a normal distribution (which symmetric). Therefore Q 2 (which is the median) is same as the mean Second quartile is $7.00 c. The 90th percentile? ← using standard values ← using Appendix C-2 ← standardizing transfomation 90th percentile is $7.45

OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 5 of 10 3.) 7.87 Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 25% below the target pressure. Suppose the target tire pressure of a certain car is 30 psi (pounds per square inch.) Target pressure = 30 Warning at = 25% a. At what psi will the TPMS trigger a warning for this car? TPMS warns when pressure is below 22.5 psi b. Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning? ← standardizing transfomation ← using Appendix C-2 There is a 0.01% probability of TPMS warning c. The manufacturer’s recommended correct inflation range is 28 psi to 32 psi. Assume the tires’ average psi is on target. If a tire on the car is inspected at random, what is the probability that the Need to find where and ← standardizing transfomation ← using Appendix C-2 ← using Appendix C-2 There is 68.26% chance that pressure is in the recommended pressure range

OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 6 of 10 4.) 7.89 Procyon Manufacturing produces tennis balls. Their manufacturing process has a mean ball weight of 2.035 ounces with a standard deviation of 0.03 ounce. Regulation tennis balls are required to have a weight between 1.975 ounces and 2.095 ounces. What proportion of Procyon’s production will fail to meet these specifications Assuming the distribution is a continuous normal distribution Fail to meat regulation is standardizing transfomation, using Appendix C-2, 4.56% of the production will fail to meet the specifications

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OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 7 of 10 5.) 7.95 Demand for residential electricity at 6:00 p.m. on the first Monday in October in Santa Theresa County is normally distributed with a mean of 4,905 MW (megawatts) and a standard deviation of 355 MW. Due to scheduled maintenance and unexpected system failures in a generating station, the utility can supply a maximum of 5,200 MW at that time. What is the probability that the utility will have to purchase electricity from other utilities or allow brownouts? Assuming the distribution is a continuous normal distribution ← standardizing transfomation ← using Appendix C-2 There is a probability of 20.33% that they will have to purchase electricity

OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 8 of 10 6.) 7.99 John can take either of two routes (A or B) to LAX airport. At midday on a typical Wednesday the travel time on either route is normally distributed with parameters μA = 54 minutes, σA = 6 minutes, μB = 60 minutes, and σB = 3 minutes. Assuming both are normal distributions a. Which route should he choose if he must be at the airport in 54 minutes to pick up his spouse? ← as 54 is the mean in route A ← using Appendix C-2 There is only 2.28% chance of arriving on time by route B where as on route A the chance is 50%. So he need to take route A . b. Sixty minutes? ← as 60 is the mean in route B ← using Appendix C-2 There is a 84.13% chance of arriving on time by route A where as on route B the chance is 50%. So he need to take route A . c. Sixty-six minutes? ← using Appendix C-2 ← using Appendix C-2 There is a 99.72% chance of arriving on time by in both route A and B. So he can take either route A or route B .

OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 9 of 10 7.) 7.100 The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 5 ml. The mean is adjustable. Assuming the distribution is a continuous normal distribution a. Where should the mean be set to ensure a 95 percent probability that a half-liter bottle will not be underfilled? needs to be satisfied If ← using Appendix C-2 Mean has to be maintained around 508.25ml to ensure that 95% of the bottles have atleast 500ml b. A 99 percent probability? needs to be satisfied If ← using Appendix C-2 Mean has to be maintained around 511.65ml to ensure that 99% of the bottles have atleast 500ml c. A 99.9 percent probability needs to be satisfied If ← using Appendix C-2 Mean has to be maintained around 515.45ml to ensure that 99.9% of the bottles have atleast 500ml

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OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 10 of 10 8.) 7.104 Among live deliveries, the probability of a twin birth is .02. This is a binomial distribution with a. In 2,000 live deliveries, what is the probability of at least 50 twin births? Both outcomes are , therefore normal approximation can be used Need to find , with continuity correction value ← using Appendix C-2 There is a 6.4% chance at least 50 twin births will be there among 2000 live births b. Fewer than 35? Need to find , with continuity correction value ← using Appendix C-2 There is a 18.9% chance that there will be less than 35 twin births among 2000 live births

OPER 5001EL 12 - Business Statistics (2022SP) Module 3 - Lesson 3 - Weekly Group Assignment Group E Page 11 of 10 9.) 7.109 On a cold morning the probability is .02 that a given car will not start in the small town of Eureka. Assume that 1,500 cars are started each cold morning . This is a binomial distribution with and Both outcomes are , therefore normal approximation can be used a. What is the probability that at least 25 cars will not start? Need to find , with continuity correction value ← using Appendix C-2 There is 84.4% chance at least 25 cars will not start in a cold morning b. More than 40? Need to find , with continuity correction value ← using Appendix C-2 There is 2.6% chance more than 40 cars will not start in a cold morning

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