Question

When Alex leaves for school 50 minutes before his class starts, the probability he makes it to class on time is estimated to be 0.75

When he leaves for class 30 minutes before it starts, the probability he makes it on time is estimated to be 0.55

If on Monday he leaves for class 50 minutes before it starts, and on Tuesday he leaves for class 30 minutes before it starts:

a.) Please fill in the table below for the Probability Distribution for the variable "The number of days Alex is on-time to class" (Hint: Make a tree diagram to start)

**Do NOT round answers on part a.)**

# of days on-time (x)	P(x)
0
1
2

**Round to TWO decimal places on parts b.) and c.)**

b.) Find the mean of this Probability distribution:  

c.) Find the Standard Deviation of this Probability distribution:

Answer 1

P(X=0)=P(leaves 30 minute before and could not make it) and P(leaves 50 minute before and could not make it)=0.25*0.45=0.1125

P(X=1)=0.75*0.45+0.25*0.55=0.475

P(X=2)=0.75*0.55=0.4125

b)

x	P(x)	xP(x)	x2P(x)
0	0.1125	0.000	0.000
1	0.475	0.475	0.475
2	0.4125	0.825	1.650
	total	1.300	2.125
	E(x) =μ=	ΣxP(x) =	1.3000
	E(x2) =	Σx2P(x) =	2.1250
	Var(x)=σ2 =	E(x2)-(E(x))2=	0.4350
	std deviation=	σ= √σ2 =	0.6595

mean =1.3000

c)

standard deviation =0.6595