4. William Paterson University conducted a study on the time faculty members spe

Question

4. William Paterson University conducted a study on the time faculty members spent commuting to campus. The study showed that the faculty members spent an average of 1.2 hours commuting, with a standard deviation of 0.40 hours and it follows the normal probability distribution.

(a) Find the portion of the faculty members who were commuting between 1.2 and 2 hours.

(b) Find the portion of the faculty members who were commuting more than 2 hours.

(c) Find the portion of the faculty members who were commuting between 2 and 2.2 hours.

(d) Find the portion of the faculty members who were commuting between 1 and 2.2 hours.

Explanation / Answer

here mean=1.2 and sd=0.4

we use standard normal variate z=(x-mean)/sd

(a) for x=1.2, z=(1.2-1.2)/0.8=0

for x=2, z=(2-1.2)/0.8=1

P(1.2<x<2)=P(0<z<1)=P(z<1)-P(z<0)=0.8413-0.5=0.3413

required answer is 0.3413

(b) P(x>2)=P(z>1)=1-P(z<1)=1-0.8413=0.1587

required answer=0.1587

(c)for x=2.2, z=(2.2-1.2)/0.8=1.25

P(2<x<2.2)=P(1<z<1.25)=P(z<1.25)-P(z<1)=0.8944-0.8413=0.0531

required answer=0.0531

(d)for x=1, z=(1-1.2)/0.8=-0.25

P(1<x<2.2)=P(-0.25<z<1.25)=P(z<1.25)-P(z<-0.25)=0.8944-0.4013=0.4931

requied answer is 0.4931

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.