Fox News reported that 5% of Americans are afraid of being alone in a house at n

Question

Fox News reported that 5% of Americans are afraid of being alone in a house at night, if a random sample of 20 Americans is selected, find the probability that: (a) There are exactly 5 people in the sample who are afraid of being alone at night. (b) There are at most 3 people in the sample who are afraid of being alone at night. (c) There are at least 3 people in the sample who are afraid of being alone at night. (d) Find the mean number of people afraid of being alone at night. 20 times 0.05-1 (e) Find the Standard Deviation of people afraid of being alone at night.

Explanation / Answer

a)

Bin(n,p) = Bin(20,0.5)

p(x) = nCx px (1-p)n-x

p(x=5) = 20C5 0.055 0.9515

= 0.002245

b)

p(x <= 3 ) = p(x=0) + p(x = 1 ) + p(x=2) + p(x=3)

= 20C0 0.050 0.9520 + 20C1 0.051 0.9519 + 20C2 0.052 0.9518 + 20C3 0.053 0.9517

= 0.3585 + 0.3774 + 0.1887 + 0.0596

= 0.9841

c)

p(x>=3) = 1- p(x<3)

= 1- p(x<=2)

= 1 -  [p(x=0) + p(x = 1 ) + p(x=2)]

= 1 - [20C0 0.050 0.9520 + 20C1 0.051 0.9519 + 20C2 0.052 0.9518 ]

= 1 - [0.3585 + 0.3774 + 0.1887 ]

= 1 - 0.9246

= 0.0754

d)

mean = n * p

= 20 * 0.05

= 1

e)

Standard deviation = Sqrt(np(1-p))

= sqrt(20 * 0.05 * 0.95)

= 0.9747

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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