statistics_final_exam_wo_solution_120423

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Fordham University *

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Electrical Engineering

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Feb 20, 2024

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Google offices based in NYC wants to ensure that its hiring practices conform to its Diversity policies and recently hired 300 engineers, of which 80% of the engineers are trainees are female. In addition, 90% of the females have a degree in electrical engineering while 78% of the males have an electrical engineering degree. A engineer is selected at random. What is the probability that the person selected is female with an engineering degree? P(female n engineering degree)=216/300 =.72 Female=240 (.8)300 Female w engineering=240(.9)=216 Google recently hired according to new Diversity policies and recently hired 300 engineers, of which 80% of the engineers are trainees are female. In addition, 90% of the females have a degree in electrical engineering while 78% of the males have an electrical engineering degree but the reminder have very specialized skills from military service. An engineer is selected at random. What is the probability that the person selected is male without an engineering degree? P(male n no engineering degree)=13.2/300 =.044 Male=60 (.2)300 Male w/o engineering=60(.22)=13.2 In Google's NYC engineering training program which fosters Diversity and which can last 18 months 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 78% of the males attended college. An engineer s selected at random to present the Diversity Program at the Annual Stockholder Meeting in February. What is the probability that the person selected is a female who did attend college? .9x.8= .72 assuming attending college and gender are independent A. P (female) P (did not attend college | female) .8x.1=.08 .8=.8x.1 B. P (did attend college) P (female | did not attend college) attended =.876 no college =.124 female no college =.08 P(female l did not attend college)=.08/.124=.645 .876x.645 =.56502 xx.9 D. P (did attend college) .72+.156 =.876 An Amazon delivery truck delivers 20 battery operated razor kits to a CVS Pharmacy store in Bronx, NY. By accident, three of the razor kits are defective because the kits were left in the rain when they were delivered and damaged 1 39847ef99790f727f71805c4ed141d1cbf9814eb.docx 12/4/23 C. P (female) P (did attend college | female) .9x.8=.72

the batteries. What is the probability that the first two razor kits sold will be returned because they are defective? (3/20) x(2/19)=.15x.11 =.0158 At the Best Buy store on Fordham Road and the Grand Concourse, they have four television brands in stock: SONY, Panasonic, Vistro and the store brand. Likewise, they also stock three amplifiers, and six speaker brands. A customer can purchase each item individually or can, for a discount, purchase a "system" " How many different systems can Best Buy offer? 4 tv options x 3 amplifier options x 6 speaker options= 72 different options McDonald's sells many things: apple pie, coffee, hamburgers, french fries and related goods. Suppose 60% of the customers at the McDonald's restaurant on Fordham Road order Big Mac, large package of french fries and a soda. If we randomly select 15 cash register receipts, what is the probability that 10 or more will show that the above three food items were ordered? (hint – use the binomial distribution) P(x> 10) n=15 p=.6 Binompdf(15, .6, 10)+ Binompdf(15, .6,11)+ Binompdf(15,.6, 12)+ Binompdf(15,.6, 13) Binompdf +(15,.6, 14) + Binompdf(15,.6, 15 )=.4032 approx. 40.32% Samsung has a huge quality management concern as 5% of the smart phones produced in their Baltimore, MD factory are defective due to dust during the final assembly . If six smart phones are randomly selected from the Baltimore assembly line , what is the probability that none of the phones are defective? (hint – use the binomial distribution) The proportion of the area under a normal curve that is to the left of z = 1.40 is _______. .9192 Used z table. ++++++++ The proportion of the area under a normal curve that is to the right of z = - 1.71 is _______. .0436 to the left 1-.0436 =.9564 Used z table. +++++++++++ The Financial Aid Department of the University wants to investigate the mean income of its part-time students to see if it was similar to a recent report titled, 120 Years of American Education. Statistical Portrait . (website: https://nces.ed.gov/pubs93/93442.pdf) The Department sample 500 part- 2 39847ef99790f727f71805c4ed141d1cbf9814eb.docx 12/4/23

time students, mostly freshman and sophomores that revealed their annual incomes were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. The number of students that earned between $27,000 and $33,000 is _____. (27000-30000)/3000=-1= .1587 (33000-30000)/3000=1=.8413 .8413-.1587 =.6826 ++++++++ General Mills is one of four major cereal manufactures in The United States and they produce and sell over 3,000,000 cartons of Cheerios cereal each year. The Quality Control Department at Cheerios set the machining tools so that the weight of a box of cereal is normally distributed with a mean of 22 ounces and a standard deviation of 0.5 ounces. The probability that a box of Cheerios weighs more than 23 ounces is ____. (23-22)/.5=2=.9772 1-.9772 =.0288-2.28% chance box weighs more than 23 oz +++++++++ At Home Depot, they sell paint. Of course there is not just one "color white" , instead, there are 14 variations of "white": pearl, glossy, ..... A homeowner would like to repaint the interior of their home in various shades of white but want to limit it to five variations How many samples of size five are possible? Ncr (14,5)=2002 options ++++++++++ ++++++++ The Internal Revenue Service has has 1,000 computers in various centers, buildings and also provide for field agents to use at home or field audits use. Each computer has a 500-gigabyte solid-state hard drive. The IRS wants to estimate the usage occupied on the hard drives as 500 gigabyte solid-state drives are double the cost of a 250 gigabyte drive. A random sample of 100 computers showed a mean of 115 gigabytes used with a standard deviation of 20 gigabytes. What is the probability that a sample mean is greater than 120 gigabytes? +++++++ The Internal Revenue Service has 1,000 computers in various centers, buildings and also provide for field agents to use at home or field audits use. Each computer has a 500-gigabyte solid-state hard drive. The IRS wants to estimate the usage occupied on the hard drives as 500 gigabyte solid-state drives are double the cost of a 250 gigabyte drive. A random sample of 100 computers showed a mean of 115 gigabytes used with a standard deviation 3 39847ef99790f727f71805c4ed141d1cbf9814eb.docx 12/4/23

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of 20 gigabytes. What is the probability that a sample mean is between 111 and 119 gigabytes? ++++++++++ The Goya Food Company specializes in food serving the Spanish and Latin- American communities. In addition to beans and rice, they recently introduced high quality olive oil (source: https://twitter.com/GoyaFoods/status/1730237565372895306/photo/1) They would like to estimate the mean daily number of gallons of olive oil sold to customers. Assume the number of gallons sold follows the normal distribution, with a population standard deviation of 5.10 gallons. A random sample of 60 days shows that the mean daily number of gallons sold is 10.00. Compute a 99% confidence interval for the population mean. ++++++++ The NY Times ran a recent series of articles on the plight of health care for the elderly - Facing Financial Ruin as Costs Soar for Elder Care (source: https://www.nytimes.com/search?query=cost+of+elder+care The United States has no coherent system for providing long-term care, leading many who are aging to struggle to stay independent or to rely on a patchwork of solutions. A local health care company wants to estimate the mean weekly elder day- care cost. A sample of 10 facilities shows a mean of $250 per week, with a standard deviation of $25. What is the 90% confidence interval for the population mean? +++++++++ A local grocery store in Bronx, NY would like to determine wants to determine the proportion of the local community who use the grocery stores proprietary cash card that offers reward points for payment. Out of 100 residents surveyed, 65 residents use the store's cash card. What is the 95% confidence interval for the population proportion? +++++++++ +++++++++++ 4 39847ef99790f727f71805c4ed141d1cbf9814eb.docx 12/4/23

The grocery store (noted above) would also like to learn how long customers browse the store within 20 minutes, with a 99% level of confidence. The population standard deviation is estimated to be 15. How large a sample is required? ++++++++ ? ++++++++++ Explain the concept of a confidence interval when estimating a population mean. ++++++ A null hypothesis makes a claim about a __________. A. Population parameter B. Sample statistic C. Sample mean D. Type II error +++++++ 5 39847ef99790f727f71805c4ed141d1cbf9814eb.docx 12/4/23

A Florida real-estate company hypothesizes that 55% residents of New York who plan to purchase a vacation residence in Florida want a condominium, A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. From the above, what is the Null Hypothesis and the Alternative Hypothesis. Please note in narrative form and equation form What decision should be made regarding the null hypothesis using the 0.01 level of significance? A. Do not reject it. B. Reject it. C. Cannot accept it or reject it based on the information given. D. Purchase a condominium. +++++++++ What is a Type II error? A Failing to reject a false null hypothesis B. Rejecting a false null hypothesis C. Accepting a false alternate hypothesis D. Rejecting a false alternate hypothesis 6 39847ef99790f727f71805c4ed141d1cbf9814eb.docx 12/4/23

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