Suppose *x* has a distribution with *μ* = 51 and
*σ* = 5.

(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
*μ*_{x} = 51 and
*σ*_{x} = 5.

Yes, the *x* distribution is normal with mean
*μ*_{x} = 51 and
*σ*_{x} = 0.3.

Yes, the *x* distribution is normal with mean
*μ*_{x} = 51 and
*σ*_{x} = 1.25.

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
*μ*_{x} = 51 and
*σ*_{x} = 1.25.

No, the sample size is too small.

Yes, the *x* distribution is normal with mean
*μ*_{x} = 51 and
*σ*_{x} = 0.3.

Yes, the *x* distribution is normal with mean
*μ*_{x} = 51 and
*σ*_{x} = 5.

Find *P*(47 ≤ *x* ≤ 52). (Round your answer to four
decimal places.)

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