Question

According to a survey, 30% of US adults attend

Answer 1

Answer:

The probability distribution of x is given by

P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ

Where n is the number of trials, x is the variable of interest and p is the probability of success.

P(x = 0) = 0.49

P(x = 1) = 0.42

P(x = 2) = 0.09

Step-by-step explanation:

The binomial distribution has the following features:

• There are n repeated trials and are independent of each other.

• There are only two possibilities: US adults attend  church every Sunday or US adults do not attend  church every Sunday

• The probability of success does not change with trial to trial.

Let x represent the  number in this sample who attend church every

Sunday, the probability distribution of x is given by

P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ

Where n is the number of trials, x is the variable of interest and p is the probability of success.

For the given case

Probability of success = p = 0.30

Number of trials = n = 2

Variable of interest = x = 0, 1, 2

For P(x = 0):

Here we have x = 0, n = 2 and p = 0.30

P(x = 0) = ²C₀(0.30⁰)(1 - 0.30)²⁻⁰

P(x = 0) = 0.49

For P(x = 1):

Here we have x = 1, n = 2 and p = 0.30

P(x = 1) = ²C₁(0.30¹)(1 - 0.30)²⁻¹

P(x = 1) = 0.42

For P(x = 2):

Here we have x = 2, n = 2 and p = 0.30

P(x = 2) = ²C₂(0.30²)(1 - 0.30)²⁻²

P(x = 2) = 0.09