Suppose x has a distribution with 𝜇 = 52 and 𝜎 = 10.
(a)
If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?
Yes, the x distribution is normal with mean 𝜇x = 52 and 𝜎 x = 2.5.Yes, the x distribution is normal with mean 𝜇x = 52 and 𝜎 x = 0.6. Yes, the x distribution is normal with mean 𝜇x = 52 and 𝜎 x = 10.No, the sample size is too small.
(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 𝜇x = 52 and 𝜎 x = 2.5.Yes, the x distribution is normal with mean 𝜇x = 52 and 𝜎 x = 0.6. Yes, the x distribution is normal with mean 𝜇x = 52 and 𝜎 x = 10.No, the sample size is too small.
Find P(49 ≤ x ≤ 53). (Round your answer to four decimal places.)