Testing the conditions, we get that [tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.
For each person sampled, there are only two possible outcomes. Either they believe in Hell, or they do not. The probability of a person believing in hell is independent of any other person, which means that the binomial distribution is used to solve this question.
Binomial distribution:
Probability of x successes on n trials, with p probability.
If [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex], it can be approximated to the normal distribution.
In this problem:
- Sample of size 100, thus [tex]n = 100[/tex].
- 58% believe in Hell, thus [tex]p = 0.58[/tex].
Then
[tex]np = 100(0.58) = 58 \geq 10[/tex]
[tex]n(1 - p) = 100(0.42) = 42 \geq 10[/tex]
[tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.
A similar problem is given at https://brainly.com/question/24261244
