Question

8. In a random sample of 16 people you find the mean time to work is 30 minutes with a variance of 49 minute find a 95% confidence interval. (10 points)

Lower Bound	Upper Bound

9. The mean number of fatal accidents between Mile markers 0 and 40 is 5 per year.

What is the probability there are a) exactly 3 fatalities b) less than 5 fatalities, c) 4 or less fatalities d) greater than 4 fatalities, greater e) Between 1 and 4 fatalities (10 points)

a	b	c	d	e

Answer 1

1)

sample mean 'x̄=	30.000
sample size   n=	16.00
sample std deviation s=	7.000
std error 'sx=s/√n=	1.7500
for 95% CI; and 15 df, value of t=		2.131
margin of error E=t*std error    =		3.73
lower bound=sample mean-E =		26.27
Upper bound=sample mean+E =		33.73

2)

this is Poisson distribution with parameter λ=5

a)

probability =

P(X=3)=

{e-λ*λx/x!}=

0.1404

b)

probability =

P(X<5)=

∑x=04 {e-λ*λx/x!}=

0.4405

c)

P(X<=4) =P(X<5) =0.4405

d)

P(X>4) =1-P(X<=4) =1-0.4405 =0.5595

e)

probability =

P(1<=X<=4)=

∑x=14 {e-λ*λx/x!}=

0.4338