Suppose x has a distribution with = 29 and = 11. (a) If random samples of size n
ID: 3065067 • Letter: S
Question
Suppose x has a distribution with = 29 and = 11.
(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 x = 29 and x = 0.7. Yes, the x distribution is normal with mean x = 29 and x = 2.75.Yes, the x distribution is normal with mean x = 29 and x = 11.
(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 x = 29 and x = 11.Yes, the x distribution is normal with mean x = 29 and x = 2.75. No, the sample size is too small.Yes, the x distribution is normal with mean x = 29 and x = 0.7.
Find P(25 x 30). (Round your answer to four decimal places.)
Explanation / Answer
The central limit theorem states that the sample mean follows approximately the normal distribution with mean µ and standard deviation /n , where µ and are the mean and standard deviation of the population from where the sample was selected. The sample size n has to be large (usually n 30) if the population from where the sample is taken is non-normal. If the population follows the normal distribution then the sample size n can be either small or large.
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
b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?
Standard deviation,
/n=11/16=2.75
Yes, the x distribution is normal with mean x = 29 and x = 2.75.
c) P(25 X 30)
Z=(X- µ)/
Z=(25-29.5)/2.75
Z=-1.45
Z=(30-29.5)/2.75
Z=0.36
P(25 X 30)=P(-1.45<Z<0.36)
P(-1.45<Z<0.36)=0.6406-0.0735=0.5671
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