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MAT150 Online Class Final Exam Student Name: Score: 1. Each person has a 75% probability of going to the Tahoe restaurant. a. You randomly select 8 people. What is the probability that 5 people will go to the restaurant? (Calculation is necessary to get FULL credits) (5 points) b. What is the probability that more than 5 people will go to the restaurant.(5 points) c. You randomly select 50 people. What is the expected value (the mean ) and standard deviation for the number of people going to the restaurant. (5 points) 2. The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $12. Find the probability that a randomly selected utility bill is between $90 and $120. (5 point) 3. A soft-drink bottle vendor claims that its process yields bottles with a mean internal strength of 157 psi (pounds per square inch) and a standard deviation of 6 psi and is normally distributed. As part of its vendor surveillance, a bottler strikes an agreement with the vendor that permits the bottler to sample from the vendor’s production to verify the vendor’s claim. (10 points) a) Suppose the bottler randomly selects 15 bottles to sample. What is the mean and standard deviation? b) Suppose the population is not normally distributed. What is the mean and standard deviation for 64 randomly selected bottles? c) What is the probability that for a sample of randomly selected 64 bottles the mean internal strength is greater than 158 psi. 4. Four students were randomly selected from a population of 10,000 students. The following are GPA for these 4 students: 2, 3, 3, 4. Suppose the population is normally distributed and the standard deviation for the population’s GPA is 0.02. (Average GPA of the population unknown) (10 points) a. Find the mean and standard deviation for GPA of the sample of four students. b. Calculate a 95% confidence interval for the populations mean GPA. 5. Find P( -1.2 < z="">< -0.2 ) (5 points) 6. a researcher wishes to find out whether there is a relationship between the age of students and their gpa. the following are ages of 4 students: 10, 11, 12, 15. the corresponding gpa are 2, 3, 3, 4. (15 point) a. use correlation formula to find the correlation coefficient r between age and gpa . b. find the equation of regression line. c. if a student’s age is 13, what is the corresponding gpa? 7. there are some people who do not think that duke will win the ncaa tournament this year. you want to measure the average intelligence of duke doubters (dd). 28 dds are randomly selected. the mean of the sample is 90 and the standard deviation is 60. calculate the 90% confidence interval for the iq of dds. assume that the population is normally distributed. (10 points) 8. it is known that the mean cholesterol level for the population of all americans is 190 and the standard deviation is 15. a researcher claims that children have an average higher cholesterol level than the national average. the researcher randomly selects 100 children and finds that the mean of cholesterol level is 198. is there enough evidence to support the researcher’s claim. you can use your own significance level α. (10 points) 9. newsweek performed a poll in which 567 american parents were asked the question, “would you prefer to have your child taught by a male or female for grades k-2?” only 12% responded that they would prefer to have their child taught by a male in grades k-2. construct a 99% confidence interval for the population proportion of american parents who prefer a male teacher for their child in k-2 grades. (10 points) 10. the tiv telephone company provides long-distance telephone service in an area. according to the company’s records, the average length of all long-distance calls placed through this company in 2015 was 12.44 minutes. the company’s management wanted to check if the mean length of the current long-distance calls is greater than 12.44 minutes. a sample of 150 such calls placed through this company produced a mean length of 13.71 minutes with a standard deviation of 2.65 minutes. using the 1% significance level, test the claim that the mean length of all current long-distance calls is greater than 12.44 minutes? (10 points) -0.2="" )="" (5="" points)="" 6.="" a="" researcher="" wishes="" to="" find="" out="" whether="" there="" is="" a="" relationship="" between="" the="" age="" of="" students="" and="" their="" gpa.="" the="" following="" are="" ages="" of="" 4="" students:="" 10,="" 11,="" 12,="" 15.="" the="" corresponding="" gpa="" are="" 2,="" 3,="" 3,="" 4.="" (15="" point)="" a.="" use="" correlation="" formula="" to="" find="" the="" correlation="" coefficient="" r="" between="" age="" and="" gpa="" .="" b.="" find="" the="" equation="" of="" regression="" line.="" c.="" if="" a="" student’s="" age="" is="" 13,="" what="" is="" the="" corresponding="" gpa?="" 7.="" there="" are="" some="" people="" who="" do="" not="" think="" that="" duke="" will="" win="" the="" ncaa="" tournament="" this="" year.="" you="" want="" to="" measure="" the="" average="" intelligence="" of="" duke="" doubters="" (dd).="" 28="" dds="" are="" randomly="" selected.="" the="" mean="" of="" the="" sample="" is="" 90="" and="" the="" standard="" deviation="" is="" 60.="" calculate="" the="" 90%="" confidence="" interval="" for="" the="" iq="" of="" dds.="" assume="" that="" the="" population="" is="" normally="" distributed.="" (10="" points)="" 8.="" it="" is="" known="" that="" the="" mean="" cholesterol="" level="" for="" the="" population="" of="" all="" americans="" is="" 190="" and="" the="" standard="" deviation="" is="" 15. a="" researcher="" claims="" that="" children="" have="" an="" average="" higher="" cholesterol="" level="" than="" the="" national="" average.="" the="" researcher="" randomly="" selects="" 100="" children="" and="" finds="" that="" the="" mean="" of="" cholesterol="" level="" is="" 198.="" is="" there="" enough="" evidence="" to="" support="" the="" researcher’s="" claim.="" you="" can="" use="" your="" own="" significance="" level="" α.="" (10="" points)="" 9.="" newsweek="" performed="" a="" poll="" in="" which="" 567="" american="" parents="" were="" asked="" the="" question,="" “would="" you="" prefer="" to="" have="" your="" child="" taught="" by="" a="" male="" or="" female="" for="" grades="" k-2?”="" only="" 12%="" responded="" that="" they="" would="" prefer="" to="" have="" their="" child="" taught="" by="" a="" male="" in="" grades="" k-2.="" construct="" a="" 99%="" confidence="" interval="" for="" the="" population="" proportion="" of="" american="" parents="" who="" prefer="" a="" male="" teacher="" for="" their="" child="" in="" k-2="" grades.="" (10="" points)="" 10.="" the="" tiv="" telephone="" company="" provides="" long-distance="" telephone="" service="" in="" an="" area.="" according="" to="" the="" company’s="" records,="" the="" average="" length="" of="" all="" long-distance="" calls="" placed="" through="" this="" company="" in="" 2015="" was="" 12.44="" minutes.="" the="" company’s="" management="" wanted="" to="" check="" if="" the="" mean="" length="" of="" the="" current="" long-distance="" calls="" is="" greater="" than="" 12.44="" minutes.="" a="" sample="" of="" 150="" such="" calls="" placed="" through="" this="" company="" produced="" a="" mean="" length="" of="" 13.71="" minutes="" with="" a="" standard="" deviation="" of="" 2.65="" minutes.="" using="" the="" 1%="" significance="" level,="" test="" the="" claim="" that="" the="" mean="" length="" of="" all="" current="" long-distance="" calls="" is="" greater="" than="" 12.44="" minutes?="" (10="">