Question

# 1.) X ~ N(60, 9). Suppose that you form random samples of 25 from this distribution....

1.) X ~ N(60, 9). Suppose that you form random samples of 25 from this distribution. Let¯¯¯¯¯XX¯ be the random variable of averages. Let ΣX be the random variable of sums. For parts c through f, sketch the graph, shade the region, label and scale the horizontal axis for¯¯¯¯¯XX¯, and find the probability. Using Excel and Excel functions for each question show me how you got your answer.

1. ¯¯¯¯¯XX¯ ~ _____(_____,_____)
2. P(¯¯¯xx¯< 60) = _____
3. Find the 30th percentile for the mean.
4. P(56 <¯¯¯xx¯< 62) = _____
5. P(18 <¯¯¯xx¯ < 58) = _____

Don't forget to use excel and the functions.

Central limit theorem:- if x follows the normal distribution with mean u and std deviation is sigma then for any n, the sample mean(xbar) follows the normal distribution with mean u & std dev (sigma/root (n))

Here X follows N(60,9) then for n =25, the sample mean xbar have mean 60 & std dev = 9 / root(25) = 9/5 = 1.8

xbar have mean 60 & std deviation 1.8

 mean std deviation 60 1.8 Question explanation Formula Probability Q.1) P(xbar < 60) NORM.DIST(60,60,1.8,1) 0.5 Q.2) 30th Percentile P30 P(xbar < a) = 0.30 NORM.INV(0.3,60,1.8) 59.06 Q.3) P(56 < xbar < 62) P(xbar < 62) - P(xbar < 56) NORM.DIST(62,60,1.8,1) - NORM.DIST(58,60,1.8,1) 0.73 Q.4) P(18 < xbar < 58) P(xbar < 58) - P(xbar < 18) NORM.DIST(58,60,1.8,1) - NORM.DIST(18,60,1.8,1) 0.13

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