Question

Suppose you are dog breeder and you want to use a confidence interval to estimate the true mean fertility levels of purebred cocker spaniels. it is known that the distribution of fertility levels of cocker spaniels is normal. how many measurements must you have in order to be sure the sampling distribution of x¯ {"version":"1.1","math":"\bar{x}"} is normal?

Answer 1

According to the Central Limit Theorem the sum or average of at least 30 independent random variables with the same distribution is approximately normal. Therefore the answer is 'at least 30 measurements.'

Answer 2

At least 30 measurements

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, a large sample size, of at least 30, can be approximated to a normal distribution with mean
`\mu` and standard deviation
`(\sigma)/(√(n))`.