Suppose x has a distribution with µ = 74 and σ = 8. If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

Options :

No, the sample size is too small.

Yes, the x distribution is normal with mean μ x = 66 and σ x = 1.5.

Yes, the x distribution is normal with mean μ x = 66 and σ x = 6.

Yes, the x distribution is normal with mean μ x = 66 and σ x = 0.4.

No, the sample size is too small.

Step-by-step explanation:

Given that:

Mean, μ = 74

Standard deviation, σ = 8

Sample size, n = 16

Based on the information given, in other to be able to make inference on the x distribution of sample means, then the size of the sample of utmost importance in statistic. Large sample sizes (usually > 30) gives are always required as sampling distribution conform to the population distribution Inn terms of mean as the sample size grows larger as the distributon becomes approximately normal.

However, the sample size given above is well below 30.hence, making it difficult to say anything about the distribution of sample means

translate k to n and reflect across the line containing jk.