Question

Suppose x has a distribution with μ = 20 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 = 20 and σ x = 1.25. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 20 and σ x = 5. Yes, the x distribution is normal with mean μ x = 20 and σ x = 0.3. (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 = 20 and σ x = 0.3. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 20 and σ x = 5. Yes, the x distribution is normal with mean μ x = 20 and σ x = 1.25. Find P(16 ≤ x ≤ 21). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 20

standard deviation = = 5

a) n = 16

= = 20

= / n = 5 / 16 = 1.25

Yes, the x distribution is normal with mean μ x = 20 and σ x = 1.25.

b) No, the sample size is too small.

P(16 21)  

= P[(16 - 20) / 1.25 ( - ) / (21 - 20) / 1.25 )]

= P( -3.20 Z 0.80)

= P(Z 0.80) - P(Z -3.20)

Using z table,  

= 0.7881 - 0.0007

= 0.7874