Question

3. The downtime per day for a certain computing facility averages 4.0 hours, with a standard deviation of 0.8 hours. a. Find the probability that the average daily downtime for a period of 30 days is between 1 and 5 hours b. Find the value of the average amount of downtime in a 30 day period such at only 10% of such 30 day periods has an average greater than that c. If the data is known to be normally distributed, what is the probability that a randomly selected day will have downtime between 1 and 5 hours?

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	4
std deviation   =σ=	0.8000
sample size       =n=	30
std error=σx̅=σ/√n=	0.1461

probability =

P(1<X<5)

=

P(-20.54<Z<6.85)=

1-0=

1.0000

b)

as top 10% values fall at 90th percentile:

for 90th percentile critical value of z=		1.28
therefore corresponding value=mean+z*std deviation=			4.19 Hours

c)

probability =

P(1<X<5)

=

P(-3.75<Z<1.25)=

0.8944-0.0001=

0.8943