Answer:
The size of the sample needed = 67.65
Explanation:
Given that :
The margin of error = 10% = 0.10
The confidence level = 90% = 0.90
Level of significance = 1 - 0.90 = 0.10
At ∝ = 0.10
Since the proportion of people that supported him/her is not given, we assumed p = 0.50
The margin of error formula can be expressed as:
Squaring both sides; we have:
n = 67.65
Therefore, the required sample size = 67.65
Using the binomial distribution, it is found that there is a:
The formula is:
The parameters are:
Researching the problem on the internet, it is found that:
The probability that both are allergic is P(X = 2), hence:
P(X = 2) = 0.06^2 = 0.0036.
0.0036 = 0.36% probability that both are allergic to pollen.
The probability of at least one is:
P(X >= 1) = 1 - P(X = 0) = 1 - 0.94^2 = 1 - 0.8836 = 0.1164.
0.1164 = 11.64% probability that at least one is allergic to pollen.
More can be learned about the binomial distribution at brainly.com/question/24863377