V- (6pts) The time needed to complete this ECO382 midterm exam is normally distr

Question

V- (6pts) The time needed to complete this ECO382 midterm exam is normally distributed with (, ). a. If 2.28% of the class can expect to complete the exam within an hour and 10 minutes or less, and if 6.68% of the class need more than an hour and 45 minutes to then what is the average time needed to complete this exam? b. What is the probability that a student will need more than one hour, but less than c. Assume that the exam's time allocation is 1.5 hours. What's the probability that a d. What is the probability that the average time spent by four randomly selected complete the same exam, What is the standard deviation? (2pts) 1.25 hours to complete this exam? (lpt) student will be unable to complete the exam within the allocated time? (1pt) students in the class to complete the examination is within the allocated time? (1pt) e. What time is exceeded by the late 495% of the students? (1pt)

Explanation / Answer

a)

P(Z<=z)=0.0228

z=-2

-2=(70-mean)/std dev.

mean-2*std dev=70

P(Z>=z)=0.0668

z=1.5

1.5=(105-mean)/std dev.

mean+1.5 std dev=105

subtract both eqns:

3.5 std dev=35

std dev=10

mean-2*10=70

mean=90

Hence,average time=90 min and standard deviation=10 min

b)P(60<x<75)

z(60)=(60-90)/10=-3

z(75)=(75-90)/10=-1.5

P(-3<=z<=-1.5)=P(z<=-1.5)-P(z<=-3)=0.0668-0.0013=0.0655

c)P(x<=90 min)

z=0

P(z<=0)=0.5

d)Again z=0,

so,P(z<=0)=0.5

e)P(Z>=z)=0.0495

P(Z<=z)=1-0.0495=0.9505

z=1.65

1.65=(x-90)/10

x=90+16.5=106.5 min

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