Question

2. Suppose it is known that 37% of people in a certain city support Candidate Y for

mayor. You randomly select 8 people from this city. Let z be the number of people in
your sample that support Candidate Y for mayor.
find the probability that x is more then or equal to 4

Answer 1

The calculated probability of more than or equal to 4 people is 0.3376

How to determine the probability of more than or equal to 4 people

From the question, we have the following parameters that can be used in our computation:

Sample, n = 8

Proportion, p = 37% = 0.37

This scenario represents the binomial experiment

And it can be calculated using

`\text{P(x)} = ^nC_x * p^x * (1 - p)^{n-x`

For the probability of more than or equal to 4 people, we have

`\text{P(x)} = \text{P(4)} + \text{P(5)} + \text{P(6)} + \text{P(7)} + \text{P(8)}`

So, we have

`\text{P(4)} = ^8C_4 * (0.37)^4 * (1 - 0.37)^{4`

`\text{P(4)} = (8!)/(4!4!) * (0.37)^4 * (1 - 0.37)^4`

P(4) = 0.2067

`\text{P(5)} = ^8C_5 * (0.37)^5 * (1 - 0.37)^3`

`\text{P(5)} = (8!)/(5!3!) * (0.37)^5 * (1 - 0.37)^3`

P(5) = 0.0971

`\text{P(6)} = ^8C_6 * (0.37)^6 * (1 - 0.37)^2`

`\text{P(6)} = (8!)/(6!2!) * (0.37)^6 * (1 - 0.37)^2`

P(6) = 0.0285

`\text{P(7)} = ^8C_7 * (0.37)^7 * (1 - 0.37)^1`

`\text{P(7)} = (8!)/(7!1!) * (0.37)^7 * (1 - 0.37)^1`

P(7) = 0.0049

`\text{P(8)} = ^8C_8 * (0.37)^8 * (1 - 0.37)^0`

`\text{P(8)} = (8!)/(8!8!) * (0.37)^8 * (1 - 0.37)^0`

P(8) = 0.0004

Add these probabilities,

So, we have

P(x ≥ 4) = 0.2067 + 0.0971 + 0.0285 + 0.0049 + 0.0004

P(x ≥ 4) = 0.3376

Hence, the probability is 0.3376