Question

Suppose x has a distribution with μ = 65 and σ = 9.

(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

No, the sample size is too small.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 9.     Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 0.6.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 2.25.

(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 = 65 and σ_x = 2.25.     Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 9.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 0.6.

Find P(61 ≤ x ≤ 66). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 65

standard deviation = = 9

n=16

= 65

=  / n = 9 / 16=2.25

es, the x distribution is normal with mean μ_x = 65 and σ_x = 2.25.

= P(61<    <66 ) = P[(61 - 65) /2.25 < ( - ) / < (66 - 65) /2.25 )]

= P( -1.78< Z < 0.44)

= P(Z <0.44 ) - P(Z <-1.78 )

Using z table,  

= 0.6700 -0.0375   

= 0.6325