28 A large number of students took a departmental math test, ofwhom 6 percent sc

Question

28 A large number of students took a departmental math test, ofwhom 6 percent scored 90 or more from the scale of 100. The scores have a bell-shaped distribution with a standard deviation of8. Ifthe minimum score to pass the test is 60, what fraction of the students failed the test? 0.0307 0.0228 0.0139 0.0096 29 The middle interval which includes 95% ofthe test scores is scores to the nearest integer.) (Round the 65 64 62 90 91 92 93 30 The passenger car tires manufactured by Greatyear Co. last on average 65,000 miles 65,000). Twelve percent (12%) oftires last more than 70,000 miles. Greatyear is considering a guarantee that will provide a discount on replacement tires ifthe original tires do not reach the guaranteed mileage. What should the guaranteed mileage be if Greatyear wants no more than (at most) 5 percent ofthe tires be eligible for the discount 56624 57991 58356 59270 31 Demand for residential electricity at a certain time period in Hamilton County is normally distributed with a mean of = 5,100 megawatts (MW) and a standard deviation = 360 MW. Due to scheduled maintenance and unexpected system failures in a generating station, the utility company can supply a maximum of 5,500 MW at that time. The probability that the utility will have to purchase electricity from other utilities or allow 0.1335 0.1162 0.1056 0.0959

Explanation / Answer

Ans:

28)

P(Z>=z)=0.06

P(Z<=z)=0.94

z=1.55

z=1.55=(90-mean)/8

mean=90-8*1.55=77.6

z(60)=(60-77.6)/8=-2.2

P(z<-2.2)=0.0139

Option c is correct.

29)95% of the data lies within 1.96 standard deviations of the mean(i.e. z=+/-1.96)

so, 77.6-1.96*8=61.92 and 77.6+1.96*8=93.28

So,rounding off to nearest integer will be 62 and 93

Option d is correct.

30)

P(Z>=z)=0.12

P(Z<=z)=0.88

z=1.17

1.17=(70000-65000)/std. dev

std. dev=5000/1.17=4255.37

P(Z<=z)=0.05

z=-1.645

x=65000-1.645*4255.37=57999.92

Option b is correct.

31)

z(5500)=(5500-5100)/360=1.11

P(z>1.11)=0.1335

option a is correct.

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