Question

The 2010 census found that 14.5% of adults in the United States identified themselves as of Hispanic origin. Q5): An opinion poll plans to interview 1000 adults at random. What are the mean and standard deviation of the sampling distribution of the proportion of individuals of Hispanic origin for samples of this size

Answer 1

The mean is
`\mu_(x) = 0.145`

The standard deviation is
`\sigma  =   0.0111`

Explanation:

From the question we are told that

The population proportion is p = 0.145

The sample size is n = 1000

Generally because the sample size is sufficiently large the mean of this sampling distribution is
`\mu_(x) = p = 0.145`

Generally the standard deviation is mathematically represented as

`\sigma  =  \sqrt{ (p(1- p ))/(n ) }`

=>
`\sigma  =  \sqrt{ ( 0.145 (1- 0.145  ))/(  1000  ) }`

=>
`\sigma  =   0.0111`