1. A companygave psychological test to prospective employees. The random variable x represents the possibletest scores. The test scores are asfollows.0 0.061 0.272 0.333 0.244 0.10 Findthe probability that a person selected at random from the surveys sample testscore of more than two. (ROUND TO TWO DECIMAL PLACES AS NEEDED)2. Afrequency distribution is shown below. Complete parts a through d.The number of dogs per household in a smalltown.DogsHouseholds0146014022164346425512(a) Usethe frequency distribution to construct a probability distribution.X P(x)0 ___1 ___2 ___3 ___4 ___5 ___(ROUND TO THE NEAREST THOUSANDTH AS NEEDED.)(b) Findthe mean of the probability distribution.(c) Findthe variance of the probability distribution.(d) Findthe standard deviation of the probability distribution.3. 47% of men consider themselves professionalbaseball fans. You randomly select 10men and ask each if he considers himself a professional baseball fans. Find the probability that the number whoconsiders themselves baseball fans is (a) exactly eight, (b) at least eight,and (c) less than eight. (c) Less thaneight. If convenient, use technology tofind the probabilities.4. 5% ofpeople in a city eligible to donate blood actually do. You randomly select four eligible blooddonors and ask them if they donate blood.X P(x)0 .8451 .1712 .0143 .0004 .000The binomial distribution for n =4and p=0.05 is shown above.Interpret the results in thecontext of the real life situation. Whatvalues of the random variable x would use consider unusual?On average, ___ eligible adults outof every 4 give blood. The standarddeviation is ___, so most samples of four eligible adults would differ from themean by at most ___ adult(s). Thevalue(s) X =2, X = 3, X=4 , or x=0, andx=1, or x=0 would be unusual because of their probabilities are equal to, more than, or less than 0.05(ROUND TO FOUR DECIMAL PLACES AS NEEDED)5. Findthe area of the indicated region under the standard normal curve.The area between z=0 and z=1.1 the standardnormal curve is ___.(On the graph not shown the z is on theright if this helps.)(ROUNDTO FOUR DECIMAL PLACES AS NEEDED)6. A surveywas conducted to measure the height of men. In the survey, respondentswere grouped by age. In the 20-29 age groups, the heights were normallydistributed, with a mean of 68.3 inches and standard deviation of 3.0inches. A study participant is randomly selected.Find the probability that is less than 65 inches. Ans: z =(65 – 68.3)/3 = -1.1P(x < 65) = P(z < -1.1) = 0.1357The probability that the study participant selected at random is less than65 inches tall is ___0.1357PART B. Find the Find the probability that his height is between 65 and 71inches.The probability that the study participantselected at random is between 65 and 71 inches tall is ___ (ROUND TO FOUR DECIMAL PLACES AS NEEDED.)7. Find the indicated z- score.The area on the graph that is shaded is 0.3745(ROUNDTO TWO DECIMAL PLACES AS NEEDED)The z-score is ___8. Find thez-score that has 10.2% of the distributions area to its right.The z-score is ___ROUNDTO TWO DECIMAL PLACES AS NEEDED)2. Ina survey of women is a certain country (ages 20-29), the mean height was 65.6inches with a standard deviation of 2.82 inches. Answer the following questions about thespecified normal distribution.(a) Whatheight represents the 98th percentile?(b) Whatheight represents the first quartile?(ROUND TO TWO DECIMAL PLACES ASNEEDED)9. Thetime spent in days waiting for a heart transplant in two states for patientswith type A+ blood can be approximated by normal distribution, as shown in thegraph.(a) What isthe shortest time spent waiting for a heart that would still place a patient inthe top 5% of waiting. ___ Days.(b) What is the longest time spent waiting for aheart would still place a patient is the bottom 15% of waiting time. ___days(ROUNDTO TWO DECIMAL PLACES AS NEEDED.)For question 7.For question 9
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