1) Let X be normally distributed with mean = 24 and standard deviation = 16. P (

Question

1) Let X be normally distributed with mean = 24 and standard deviation = 16.

  P(8 X 32) =

Find x such that P(X x) = 0.9382. (Round "z" value to 2 decimal places, and final answer to nearest whole number.)

Find x such that P(X > x) = 0.025. (Round "z" value to 2 decimal places, and final answer to nearest whole number.)

Find x such that P(2,700 X x) = 0.1217. (Round "z" value to 2 decimal places, and final answer to nearest whole number.

Find x such that P(X x) = 0.484. (Round "z" value to 2 decimal places, and final answer to nearest whole number.)

Find the population mean if the population standard deviation = 16. (Round "z" value and final answer to 2 decimal places.)

Find the population mean if the population standard deviation = 22. (Round "z" value and final answer to 2 decimal places.)

Find the population standard deviation if the population mean = 163. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

Find the population standard deviation if the population mean = 153. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

Standard deviation =

1) Let X be normally distributed with mean = 24 and standard deviation = 16.

Explanation / Answer

for z=(X-mean)/std deviation

a) P(X<0) =P(Z<-1.5)=0.0668

b)P(X>4)=1-P(Z<-1.25)=1-0.10565 =0.89435

c)P(4<X<28)=P(-1.25<Z<0.25)=0.5987-0.10565 =0.4931

d)P(8<X<32)=P(-1<Z<0.5)=0.6915-0.1587=0.5328

2)a)P(X<x)=0.9382

z=1.5398

hence X=mean +z*std deviation =4085.854

b)z=1.96

x=4463.968

c)z=0.3099

X=2978.954

d)P(X<x)=0.484

z=-0.04

x=mean +z*std deviation =24+(-0.04)*16=23.36

3)a)z=1.0803

hence mean=184-16*1.0803+=166.7149

b)mean =160.233

c)std deviation=19.439

d)28.6952

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