Question

The time required for a student to complete an Economics 110 exam is normally distributed with a mean of 54 minutes and a standard deviation of 16 minutes.

5. ______ What percentage of students will complete the exam in less than 75 minutes (before end of class period)? (A) .4049 (B) .9951 (C) .8051 (D) .9049

6. ______ At what point in time (i.e., how long after the exam starts) will one-third of all students have finished taking the exam? (A) 25 minutes (B) 60.9 minutes (C) 47.1 minutes (D) 38.5 minutes

7. ______ In a class of 50 students taking an Economics 110 exam, what is the probability that the average time required to take the exam will be more than 60 minutes? (A) .4960 (B) .0040 (C) .1480 (D) .3520

Answer 1

5) P(X < 75)

= P((X - )/ < (75 - )/)

= P(Z < (75 - 54)/16)

= P(Z < 1.31)

= 0.9049

Option - D is correct.

6) P(X < x) = 0.3333

Or, P((X - )/ < (x - )/) = 0.3333

Or, P(Z < (x - 54)/16) = 0.3333

Or, (x - 54)/16 = -0.43

Or, x = -0.43 * 16 + 54

Or, x = 47.1

Option - C is correct.

7) P( > 60)

= P(( - )/() > (60 - )/())

= P(Z > (60 - 54)/(16/))

= P(Z > 2.65)

= 1 - P(Z < 2.65)

= 1 - 0.9960

= 0.0040

Option - But is correct.