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
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