Question

random variable x has a Normal distribution, N(75,25). P(65<X<80) = ______________ .

Random variable Y has a Binomial Distribution, B(8, 0.5). P(Y<5) = ______________ .

Let P(A)=0,6, P(B)=0.4, and P(A and B ) = 0.88, P(A and B) = _____________ .

For events A,B, C, P(A)=0.2, P(B)=0.1, and P(C)=0.6, then what is the range of P(A or B or C)? ___________ .

Answer 1

Answer:

1.

Given,

Mean = 75

Standard deviation = sqrt(25)

= 5

P(65 < X < 80) = P((65 - 75)/5 < (x-u)/s < (80 - 75)/5)

= P(-2 < z < 1)

= P(z < 1) - P(z < -2)

= 0.8413447 - 0.0227501 [since from z table]

= 0.8186

2.

Given,

n = 8

p = 0.5

P(Y < 5) = P(0) + P(1) + P(2) + P(3) + P(4)

Binomial distribution P(X = x) = nCx*p^x*q^(n-x)

= 8C0*0.5^0*0.5^8 + 8C1*0.5^1*0.5^7 + 8C2*0.5^2*0.5^6 + 8C3*0.5^3*0.5^5 + 8C4*0.5^4*0.5^4

= 0.0039 + 0.0313 + 0.1094 + 0.2188 + 0.2734

P(Y < 5) = 0.6368

Please post the remaining question as separate post. Thank you.