Question

A random sample of size 32 was taken from an exponentially distributed population with a population mean 25 and a population standard deviation 6. (Note: an exponential distribution is a right skewed distribution).

Determine each of the following:

a) What range best describes P(X<23.97) ?

1. Less than 0.5

2. Greater than 0.5

3. Cannot be determined

b) What range best describes P(Xˉ<23.97) ? ...*** Note Xˉ meaning the x with the - on top of it ***

1. Less than 0.5

2. Greater than 0.5

3. Cannot be determined

Answer 1

a)

P(X<23.97)=1-exp(-23.97/25)=

0.6166

2. Greater than 0.5

b)

for normal distribution z score =(X-μ)/σx

mean μ=	25
standard deviation σ=	25
sample size       =n=	32

std error=σx̅=σ/√n=

4.41942

probability =P(X<23.97)=(Z<(23.97-25)/4.419)=P(Z<-0.23)=0.409

1. Less than 0.5