Question

In a religious survey of southerners, it was found that 65% believe in angels. If you have a random sample of 8 southerners: What is the probability that at most 3 of the southerners believe in angels

Answer 1

10.60%

Explanation:

We have to solve the above we have to apply bimonial and add each one, like this:

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

p (x <= 3) = 8C0 * (0.65) ^ 0 * (0.35) ^ 8 + 8C1 * (0.65) ^ 1 * (0.35) ^ 7 + 8C2 * (0.65) ^ 2 * (0.35) ^ 6 + 8C3 * (0.65) ^ 3 * (0.35) ^ 5

p (x <= 3) = 8! / (0! (8-0)!) * (0.65) ^ 0 * (0.35) ^ 8 + 8! / (1! (8-1)!) * (0.65 ) ^ 1 * (0.35) ^ 7 + 8! / (2! (8-2)!) * (0.65) ^ 2 * (0.35) ^ 6 + 8! / (3! (8-3)!) * (0.65) ^ 3 * (0.35) ^ 5

p (x <= 3) = 0.1060

therefore the probability is 10.60%

Answer 2

The probability that at most 3 of the southerners believe in angels is 10.61%

Explanation:

Given;

65% believe in angels = p

then, 35% will not believe in angel = q

total sample number, n = 8

The probability that at most 3 southerners believe in angels is calculated as;

= p( non believe in angel) or p( 1 southerner believes and 7 will not believe) or p( 2 southerner believe and 6 will not believe) or p( 3 southerner believe and 5 will not believe)

= 8C₀(0.65)⁰(0.35)⁸ + 8C₁(0.65)¹(0.35)⁷ + 8C₂(0.65)²(0.35)⁶ + 8C₃(0.65)³(0.35)⁵

= 1(1 x 0.000225) + 8(0.65 x 0.000643) + 28(0.4225 x 0.00184) + 56(0.2746 x 0.00525)

= 0.1061

= 10.61%

Therefore, the probability that at most 3 of the southerners believe in angels is 10.61%