Question

# A random variable X is normally distributed. It has a mean of 254 and a standard...

A random variable X is normally distributed. It has a mean of 254 and a standard deviation of 21.

List the givens with correct symbols:

? (σ N X̄ μ s X p n) = 254

? (X̄ n σ s X p μ N) = 21

a) If you take a sample of size 21, can you say what the shape of the sampling distribution for the sample mean is?

? Yes No

Why or why not? Check all that apply.

• σσ is unknown
• σσ is known
• n is less than 30
• population is normal
• n is at least 30
• population is not normal

b) For a sample of size 21, state the mean and the standard deviation of the sampling distribution of the sample mean.

mean of the sampling distribution of the sample mean when n = 21:

standard deviation of the sampling distribution of the sample mean when n = 21:

Round final answer to two decimal places

The correct symbols are

μ = 254

σ = 21

a)

Here I take sample of 21 1000 times and in c22 row I found the mean of that 21 samples so the shape of sampling distribution for the sample mean is again a normal shape.

Here the parent population is normal we are taking samples from Normal population so the sampling distribution for sample mean is again normal shape.

b)

Here

mean of the sampling distribution of the sample mean when n = 21: 253.98

standard deviation of the sampling distribution of the sample mean when n = 21: 4.61

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