Question 2 Use the Z-table in the formula sheet to answer the following question

Question

Question 2

Use the Z-table in the formula sheet to answer the following question: The school encourages its students to form a habit of self-learning. Records in the school indicate that the mean amount of time undergraduate students study per week on the learning system is 10 hours. The hours studied follows the normal distribution with a standard deviation of 2 hours.

(a) What percent of students study less than 8 hours per week on the learning system? (5 marks)

(b) There are about 10% of students who study more than H hours per week on the learning system, what is the value of H? (5 marks)

(c) Suppose we select a random sample of 100 current students. What is the probability that the mean of this sample is no more than 9.75 hours? (5 marks)

Explanation / Answer

SOLA:

Mean=10

sd=2

P(X<8)

z=x-mean/sd

=8-10/2

=-1

P(Z<-1)

pnorm(-1)

0.1586553

= 0.1586553*100

=15.86553

=15.87%

15.87 percent of students study less than 8 hours per week on the learning system.

Solutionb:

for 10 percentile z=-1.282

z=x-mean/sd

x-10/2=-1.282

x=-1.282*2+10

x= 7.436

the value of H=7.436

Solutionc:

P(X<9.75)

z=9.75-10/2

= -0.125

P(Z<=-0.125)

pnorm( -0.125)

0.4502618

a random sample of 100 current students.

n=100

np=100* 0.4502618

=45.02618

=45

ANSWER:45

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