Question

Suppose x has a distribution with μ = 35 and σ = 20.

(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 = 35 and σ_x = 1.3.Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 5.    No, the sample size is too small.Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 20.

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?

No, the sample size is too small.Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 1.3.    Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 5.Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 20.

Find P(31 ≤ x ≤ 36). (Round your answer to four decimal places.)

Answer 1

SOLUTION:

From given data,

Suppose has a distribution with μ = 35 and σ = 20.

Mean = μ =35,

Standard deviation = σ = 20

(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 = 35 and σ_x = 1.3.

Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 5.   

No, the sample size is too small.

Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 20.

sample of size = n = 16,

sample mean = μ =35

sample standard deviation = σ = 20

The x distribution of sample means

μ = μ_x = 35

σ_x = σ / = 20 / = 5

Correct option is,

Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 5.   

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?

No, the sample size is too small.

Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 1.3.

   Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 5.

Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 20.

   Yes, the x distribution is normal with mean μ_x = 35 and σ_x = 5.

Find P(31 ≤ x ≤ 36). (Round your answer to four decimal places.)

P(31 ≤ x ≤ 36)

Z = (x  - ) / ( / )

At x = 31

Z = (x  - ) / ( / )

= (31- 35) / (20 / )

=  -4 / 5

= - 0.8

At x = 36

Z = (x  - ) / ( / )

= (36- 35) / (20 / )

= 1 / 5

= 0.2

P(31 ≤ x ≤ 36) = P(- 0.8 ≤ z ≤ 0.2)

= P(z ≤ 0.2) - P(z ≤ - 0.8)

= 0.57926 - 0.21186

= 0.3674

P(31 ≤ x ≤ 36) = 0.3674   (Round your answer to four decimal places.)