The time to complete a set of homework problems has a normal distribution with m

Question

The time to complete a set of homework problems has a normal distribution with mean 42 minutes and standard

deviation 9 minutes.

a) Find the probability that a randomly selected student will complete the homework problems in less than

30 minutes.

A. 0.4082 B. 0.0918 C. 0.4032 D. 0.9082 E. 0.133

b) One would expect 10% of students to complete their homework in more than ____ minutes.

A. 55.0 B. 45.6 C. 43.4 D. 53.5 E. 1.28

c) For a random sample of 36 students, find the probability that the SAMPLE MEAN completion time is

greater than 45 minutes.

B.0.4772 B. 0.1293 C. 0.3707 D. 0.0228 E. 0.9772

Explanation / Answer

mean is 42 and sd is 9

a) P(x<30)=P(z<(30-42)/9)=P(z<-1.33) or 1-P(z<1.33) from normal distribution table we get 1-0.9082=0.0918 option B

b) z value for 10% is given from 90% area under curve as 1.28 ( from normal distribution table look for 0.9 in area and find the corresponding z value)

thus 42+1.28*9=53.52 option D

c) P(xbar>45)=P(z>(45-42)/(9/sqrt(36))=P(z>2) or 1-P(z<2)

from normal distribution table we get 1-0.9772 or 0.0228 answer D

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