Let X 1 , X 2 , ..., X 50 is a sample distribution with mean 2 and variance 16.

Question

Let X1, X2, ..., X50 is a sample distribution with mean 2 and variance 16.

Just question 2 please. Trying to see if I did it correctly.

1. (12 points) Suppose that your daily expenses X are normally distributed with mean $25 and standard deviation $4. KNorm (2s, 12 (b) Sketch the graph of the pdf. (2) Write the pdf SQL (x-2s a FX) 2m 4) 25 Find the probability that, in a randomly selected day, you spend (c) no more than $10. PCX410) .884 ODD To 23 (d) between $30 and $40. PC 30 LX40) SSD 40 2X 2.6393 (e) Find E (25 - and Var 25 )-(-4)-l Era - the 25- ) LaVar () - 3 , 2. (18 points) Let X1, X2, ..., X50 is a sample from a distribution with mean 2 and variance 16. (z, so (a) What is the distribution of X a (b) Find P(1

Explanation / Answer

2) for average of 50 numbers =mean =2

and variance =(42)/50 =16/50

a)hence distribution of Xbar ~ N(2,16/50)

b) for std error of mean =(16/50)1/2 =0.5657

P(1<Xbar<2)=P((1-2)/0.5657<Z<(2-2)/0.5657)=P(-1.7678<Z<0)=0.5-0.0385=0.4615

c) for expected sum of 50 numbers =2*50 =100

and varriance =50*16 =800

hece distribution of S50 ~ N(100 ,800)

d)here std deviation of sum =(800)1/2 =28.2843

P(100<S50 <150)=P((100-100)/28.2843<Z<(150-100)/28.2843)=P(0.00<Z<1.7678)=0.9615-0.5 =0.4615

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