A random sampleX1;X2; ... ;X150 is drawn from a population with mean = 40 and st

Question

A random sampleX1;X2; ... ;X150 is drawn from a population with mean
= 40 and standard deviation = 15. Let U =(X1+X2+...+X50)=50 represent the sample mean
of the first 50 observations and V = (X51 + X52 + ... +X150)=100 the sample mean of the last 100
observations.
(a) If the population distribution is unknown, what are theapproximate distributions of U and V ?
Which probability would you expect to be larger, P(35 <=U <= 45) or P(35 <= V <= 45)? Why?
(b) If the population is normally distributed, what are thedistributions of U and V ? Which
probability would you expect to be larger, P(35 <= U <= 45)or P(35 <= V<= 45)? Why? Any idea or suggestion will be highly appreciated. A random sampleX1;X2; ... ;X150 is drawn from a population with mean
= 40 and standard deviation = 15. Let U =(X1+X2+...+X50)=50 represent the sample mean
of the first 50 observations and V = (X51 + X52 + ... +X150)=100 the sample mean of the last 100
observations.
(a) If the population distribution is unknown, what are theapproximate distributions of U and V ?
Which probability would you expect to be larger, P(35 <=U <= 45) or P(35 <= V <= 45)? Why?
(b) If the population is normally distributed, what are thedistributions of U and V ? Which
probability would you expect to be larger, P(35 <= U <= 45)or P(35 <= V<= 45)? Why? Any idea or suggestion will be highly appreciated. Any idea or suggestion will be highly appreciated.

Explanation / Answer

Do you mean U=X1+...+X50=50 or U=X1+...+X50/50?????

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