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 (, 2) a. If 15.87% of the class can expect to complete the exam within 1 hour and 10 minutes or less, and if 668% of the class need more than 1 hour and 35 minutes to complete the same standard deviation? (2pts) exam, then what is the average time needed to complete the exam? What is the but less than 1.25 hours? (1pt) probability that a student will be unable to complete the exam within that time? (Ipt) students in the class to complete the examination is within the exam allocated time? (1pt) b. What is the probability that a student will complete the exam in more than hour, c. Assume that the time allocated is an hour and fourty minutes. What's the d. What is the probability that the average time spent by four randomly selected e. What time is exceeded by the late 4.95% of the students? (1pt)

Explanation / Answer

here let mean =a minute and std deviation is b minute.

for 15.87 percentile ; zscore =-1

hence a-b =70 minutes ............(1)

for 6.68% top time at(100-6.68=93.32) percentile ; z score =1.5

henc e a+1.5 b =95 ----------------(2)

solving equation 1 and 2

std deviation b=10

and mean a=80

b) P( 1hour <X<1.25 hour)=P(60 minute<X<75 minute) =P((60-80)/10<Z<(75-80)/10)=P(-2<Z<-0.5)

=0.3085-0.0227 =0.2858

c)P(X>1 hr 40 minute)=P(X>100) =P(Z>2)=2.28%

d)here std error of mean =std deviation/(n)1/2=10/(4)1/2 =5

hence P(X<100)=P(Z<(100-80)/5)=P(X<4) =0.99997

e) for top 4.95% ; z=1.6497

hence corresponding score =80+1.6497*10=96.50

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