Question

Suppose x has a distribution with μ = 78 and σ = 17.

(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 = 78 and σ_x = 4.25.Yes, the x distribution is normal with mean μ_x = 78 and σ_x = 1.1.     Yes, the x distribution is normal with mean μ_x = 78 and σ_x = 17.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 = 78 and σ_x = 1.1.No, the sample size is too small.     Yes, the x distribution is normal with mean μ_x = 78 and σ_x = 4.25.Yes, the x distribution is normal with mean μ_x = 78 and σ_x = 17.

Find P(74 ≤ x ≤ 79). (Round your answer to four decimal places.)

Answer 1

solution

μ = 78

σ = 17

n = 16

= 78

= / n = 17 / 16=4.25

Yes, the x distribution is normal with mean μ_x = 78 and σ_x = 4.25.

(b) = / n = 17 / 16=4.25

Yes, the x distribution is normal with mean μ_x = 78 and σ_x = 4.25.

P(74 ≤ x ≤ 79) = P[(74 - 78) / 4.25< ( - ) / < (79 - 78) /4.25 )]

= P(-0.94 < Z < 0.24)

= P(Z <0.24 ) - P(Z <-0.94 )

Using z table,  

= 0.5948 - 0.1736

= 0.4212