1. Find the area under the standard normal curve between z = 0 and z = 3. (a) (b) (c) (d)

Size: px

Start display at page:

Download "1. Find the area under the standard normal curve between z = 0 and z = 3. (a) (b) (c) (d)"

Ronald Simon
6 years ago
Views:

1 STA 2023 Practice 3 You may receive assistace from the Math Ceter. These problems are iteded to provide supplemetary problems i preparatio for test 3. This packet does ot ecessarily reflect the umber, type, or topics of problems that will appear o the actual test, or is it guarateed to cover every topic that may appear o the test. Be sure to study all assiged homework problems. Part I Multiple Choice 1. Fid the area uder the stadard ormal curve betwee z = 0 ad z = 3. (a) (b) (c) (d) Fid the area uder the stadard ormal curve to the right of z = 1. (a) (b) (c) (d) For a stadard ormal curve, fid the z-score that separates the bottom 90% from the top 10%. (a) 1.28 (b) 0.28 (c) 1.52 (d) For a stadard ormal curve, fid the z-scores for which 90% of the distributio s area lies betwee z ad z. (a) ( 1.28, 1.28) (b) ( 1.645, 1.645) (c) ( 1.96, 1.96) (d) ( 0.90, 0.90) 5. IQ test scores are ormally distributed witha mea of 101 ad a stadard deviatio of 20. A idividual s IQ score is foud to be 111. Fid the z-score correspodig to this value. (a) (b) 2.00 (c) 0.5 (d) Suppose that prices of a certai model of ew homes are ormally distributed with a mea of $150,000 ad a stadard deviatio of $1100. Fid the percetage of buyers who paid betwee $148,900 ad $151,100. (a) 68% (b) 34% (c) 32% (d) 47.5% 7. A physical fitess associatio is icludig the mile ru i its secodary-school fitess test. The time for this evet for boys i secodary school is kow to possess a ormal distributio with a mea of 460 secods ad a stadard deviatio of 60 secods. The fitess associatio wats to recogize the fastest 10% of the boys with certificates of recogitio. What time would the boys eed to beat i order to ear a certificate of recogitio from the fitess associatio? (a) 537 secods (b) 383 secods (c) 361 secods (d) 559 secods

2 8. The amout of moey collected by the sack bar at a large uiversity has bee recorded daily for the past five years. Records idicate that the mea daily amout collected is $4650 ad the stadard deviatio is $400. The distributio is skewed to the right due to several high volume days (football game days). Suppose that 100 days were radomly selected from the five years ad the average amout collected from those days was recorded. Which of the followig describes the samplig distributio of the sample mea? (a) ormally distributed with a mea of $4650 ad a stadard deviatio of $400. (b) ormally distributed with a mea of $465 ad a stadard deviatio of $40. (c) skewed to the right with a mea of $4650 ad a stadard deviatio of $400. (d) ormally distributed with a mea of $4650 ad a stadard deviatio of $40. Part II 9. The amout of cor chips dispesed ito a 14-ouce bag by the dispesig machie has bee idetified as possessig a ormal distributio with a mea of 14.5 ouces ad a stadard deviatio of 0.3 ouces. Suppose 100 bags of chips were radomly selected from this dispesig machie. Fid the probability that the sample mea weight of these 100 bags exceeded 14.6 ouces. 10. A simple radom sample of size = 25 is draw from a populatio that is ormally distributed with populatio stadard deviatio σ = 17, ad the sample mea, x, is 123. Costruct a 94% cofidece iterval to estimate the mea.

3 11. A Gallup poll coducted December 20-21, 1999 asked Americas how may hours of TV they watch durig the week. How may subjects would be eeded i order to estimate the umber of hours of TV Americas watched withi 0.5 hours with 95% cofidece? Iitial survey results idicate that σ = Compute the mea ad stadard deviatio (to three decimal places) of the radom variable X whose probability distributio is x P (X = x) To play a certai gamblig game, a player wagers $2. The probability of wiig is 0.025, with a payoff of $50, a et gai of $48. The probability of losig is 0.975, for a loss of $2. Fid ad iterpret the expected value (to the player) of this game. 14. Depakote is a medicatio whose purpose is to reduce the pai associated with migraie headaches. I cliical trials ad exteded studies of Depakote, 2% of the patiets i the study experieced weight gai as a side effect. Let X, a biomial radom variable, be the umber of patiets who experiece weight gai as a side effect. (a) Compute the mea ad stadard deviatio of the radom variable X, the umber of patiets experiecig weight gai i 600 trials of the probability experimet. (b) Iterpret the mea.

4 (c) Would it be uusual to observe 16 patiets who experiece weight gai i a radom sample of 600 patiets who take the medicatio? Why? 15. Mark Price holds the record for percetage of free throws made i the atioal Basketball Associatio, at 90.4%. Assumig that free throws are idepedet evets, compute the probability that i his ext 10 free throws (a) Mark Price makes exactly 8. (b) Mark Price makes 8 or more. (c) Mark Price makes fewer tha 7. (d) Mark Price makes betwee 6 ad 8, iclusive. 16. A stadardized test has a mea score of µ = 1000 ad a stadard deviatio of σ = 150. Fid the test score that correspods to the 80 th percetile.

5 For each of the followig, determie whether a biomial radom variable is beig described. Circle yes if the variable is a biomial radom variable, ad circle o if it is ot. 17. Hak The Tak Wilso claims he ca eat more hot dogs tha ayoe else. To prove his claim, The Tak eats hot dogs util he gets sick. The umber of hot dogs he eats is recorded. YES O 18. For a particular airlie, the probability that a radomly selected flight will arrive o time is A radom sample of 100 flights is selected, ad the umber of o-time flights is recorded. (Assume idepedece) YES O 19. Accordig to ielso Media Research, 75% of all Uited States households have cable televisio. I a small tow of 40 households, a radom sample of 10 households is asked whether they have cable televisio. The umber of households with cable televisio is recorded. YES O 20. A persoel director wishes to estimate the mea scores for a proposed aptitude test that may be used i screeig applicats for clerical positios. Usig a sample of = 100 applicats, she foud x = 75.6 ad s = Costruct a 95% cofidece iterval estimate for the true mea. 21. A large casualty isurace compay is revisig its rate schedules. A staff actuary wishes to estimate the average size of claims resultig from fire damage i apartmet compleses havig betwee 10 ad 20 uits. The curret year s claim-settlemet experiece will be used as a sample. There were 19 claim settlemets for buildigs i this category. The average claim size was $73,249 with a stadard deviatio of $37,246. Costruct a 90% cofidece iterval estimate of the mea claim size. 22. The highway patrol director i a certai state has ordered a crackdow o druke drivers. To see if his safety campaig is workig, the director has ordered a samplig study to estimate the proportio of all fatal traffic accidets caused by drikig. I a radom sample of = 100 accidets, 42 percet were attributable to alcohol. Assumig that the accidet ppopulatio is large, costruct a 95% cofidece iterval for the populatio proportio of accidets caused by druk drivig.

6 Formula Page µ = x σ = (xi µ) 2 x = x s = (xi x) 2 1 µ = xi f i σ = (xi µ) 2 f i x = xi f i z = x µ σ s = (xi x) 2 f i 1 z = x x s P (A) + P (A) = 1 P (A B) = P (A ad B) P (B) P (A or B) = P (A) + P (B) P (A ad B) P (A ad B) = P (A) P (B A) E(X) = µ = x P (X = x) E(X) = µ = p σ 2 = (x µ) 2 P (X = x) C r =! r!( r)! σ 2 = pq P (X = x) = C x p x q ( x) σ x = σ σˆp = p q z = x µ σ x x ± z α/2 σ ( zα/2 σ = E ) 2 t = x µ s/ x ± t α/2 s z = ˆp p p q ˆp ± z α/2 = ˆp ˆq ˆp ˆq ( zα/2 ) 2 E

A point estimate is the value of a statistic that estimates the value of a parameter.

A point estimate is the value of a statistic that estimates the value of a parameter. Chapter 9 Estimatig the Value of a Parameter Chapter 9.1 Estimatig a Populatio Proportio Objective A : Poit Estimate A poit estimate is the value of a statistic that estimates the value of a parameter.