Question

Suppose x has a distribution with μ = 70 and σ = 9. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

Answer 1

The x distribution of sample means can be described using the Central Limit Theorem. As the sample size increases, the distribution of sample means approaches a normal distribution. This holds true for random samples of size n = 16.

Step-by-step explanation:

The x distribution of sample means can be described using the Central Limit Theorem. According to the Central Limit Theorem, as the sample size increases, the distribution of sample means approaches a normal distribution, regardless of the shape of the original population distribution. This means that for random samples of size n = 16, the distribution of sample means will be approximately normal, even if the distribution of x is not normal.

Answer 2

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.
(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?
Yes, the x distribution is normal with mean μ x = 66 and σ x = 0.4.
Yes, the x distribution is normal with mean μ x = 66 and σ x = 1.5.
No, the sample size is too small.
Yes, the x distribution is normal with mean μ x = 66 and σ x = 6..
Find P(62 ≤ x ≤ 67). (Round your answer to four decimal places.)