Question

fee? 5) Amon g coffee drinkers, men drink a mean of 3.4 cups per day with a standard deviation of 0.8 cup. Assum distribution. e the number of cups per day follows a normal a. What proportion drinks 2 cups per day or more? b. What proportion drinks no more than 4 cups per day?

Answer 1

5a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	3.2
std deviation   =σ=	0.800

probability =

P(X>2)

=

P(Z>-1.5)=

1-P(Z<-1.5)=

1-0.0668=

0.9332

b)

probability =

P(X>4)

=

P(Z>1)=

1-P(Z<1)=

1-0.8413=

0.1587

c)

for top 5% critical z=1.645

hence corresponding number of coffee cups=mean+z*std deviation=3.2+1.645*0.8 =4.52

d)

sample size       =n=	20
std error=σx̅=σ/√n=	0.1789

probability =

P(X>3)

=

P(Z>-1.12)=

1-P(Z<-1.12)=

1-0.1314=

0.8686