203k views
5 votes
Mean and standard deviation of senior citizens in the 2010 US Census. We learn that 13% of all people in the US are senior citizens. Let the random variable X represent the number of senior citizens in a random sample of 10 people. Find the mean and standard deviation of this random variable.

1. Mean (μ) of X:
2. Standard Deviation (σ) of X:

Choose the correct values from the options below:

a) μ = 1.3, σ = 1.14
b) μ = 1.3, σ = 1.07
c) μ = 1.7, σ = 1.14
d) μ = 1.7, σ = 1.07

1 Answer

0 votes

Final answer:

The mean (μ) for the random variable representing the number of senior citizens in a sample of 10 people is 1.3, and the standard deviation (σ) is approximately 1.07.

Step-by-step explanation:

The question asks us to find the mean (μ) and standard deviation (σ) of the random variable X, which represents the number of senior citizens in a random sample of 10 people from a population where 13% are senior citizens. To find these statistics, we assume a binomial distribution because each person in the sample can be classified as a senior or not.

The mean μ of X is found using the formula μ = np, where n is the sample size and p is the probability of success (in this case, being a senior citizen).

Mean: μ = n * p = 10 * 0.13 = 1.3

The standard deviation σ of X is found using the formula σ = √(np(1-p)), which includes the probability of failure (1-p).

Standard Deviation: σ = √(10 * 0.13 * (1-0.13)) σ = √(10 * 0.13 * 0.87) σ = √(1.131) σ ≈ 1.07

Therefore, the correct option is b) μ = 1.3, σ = 1.07.

User Jdmorgenstein
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories