Based on gathered data by the marketing branch of Major Telecommunications Enter

Question

Based on gathered data by the marketing branch of Major Telecommunications Enterprises
indicate that 65% of engineering professionals own a cell phone.

a) If a random sample of 10 engineering professionals is selected, what is the
probability that at least 7 own a cell phone?

b) If a random sample of 15 engineering professionals is selected, what is the
probability that more than 6 but fewer than 10 own a cell phone?

c) Assume now that a random sample of 2,000 engineering professionals is
selected. What is the probability that more than 1,315 own a cell phone?

Explanation / Answer

a)

X~ bin(10,0.65)

p(x>=7) = p(x=7) +p(x=8) + p(x=9) + p(x=10)

= 10C7 0.657 0.353 + 10C8 0.658 .352+ 10C9 0.6590.35 + 10C10 0.6510 0.350

= 0.2522+0.1757+0.0725+0.0135

= 0.5139

b)

E(x) = np = 15*0.65 = 9.75 , var(x) = npq = 15*0.65*0.35=3.4125

p(6<x<10) = p(x<10) - p(x<6) (BY using continuty correction to normal)

= p(x<9.5) - p(x<5.5)

= p(z<9.5 - 9.75/sqrt(3.4125)) - p( z< 5.5 - 9.75/sqrt(3.4125))

= p(z< -0.1353) - p(z<-2.301)

= (1 - P(z<0.1353)) - (1-p(z< 2.301))

= 0.44619-0.01070

= 0.43549

c)

p = 0.65 , n = 2000

E(x) = np = 1300, var(x) = np(1-p) = 455

p(x>1315) = p(z> 1315.5 - 1300 / sqrt(455))

= p( z> 0.7267)

= 1-p(z<0.7267)

= 0.2337

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

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