In: Math
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 μx = 65 and σx = 9. Yes, the x distribution is normal with mean μx = 65 and σx = 0.6.Yes, the x distribution is normal with mean μx = 65 and σx = 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 μx = 65 and σx = 2.25. Yes, the x distribution is normal with mean μx = 65 and σx = 9.Yes, the x distribution is normal with mean μx = 65 and σx = 0.6.
Find P(61 ≤ x ≤ 66). (Round your answer to four
decimal places.)
Solution :
Given that,
mean = = 65
standard deviation = = 9
n=16
= 65
= / n = 9 / 16=2.25
es, the x distribution is normal with mean μx = 65 and σx = 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