Question

Exander’s drive from home to work takes and average of 19 minutes normally distributed, with a standard deviation of 3 minutes.

What is the probability that a trip will take 18 minutes or less?

0.6915

0.93

0.3694

0.3085

What is the probability that a trip will take 21 minutes or more?

0.8413

0.2525

0.1587

0.7468

What is the probability that a trip will take between 14 and 17 minutes?

0.5328

0.467

0.2047

0.2122

What is the probability the trip will take exactly 15 minutes?

0

0.040

0.712

0.500

Answer 1

mean=19

Std dev=3

X~N(19,3²)

1) Z=(18-19)/3=-0.3333

P(Z<-0.333)=0.3694

2) Z=(21-19)/3=0.6666

P(Z>0.6666)=1-P(z<0.6666)=1-0.7475=0.2525

3)14<Z<17

Z=(14-19)/3=-1.6666

Z=(17-19)/3=-0.6666

P(-1.6666<Z<-0.6666)=P(Z<-0.6666)-P(Z<-1.6666)=0.253-0.0483=0.2047

4)Z=(15-19)/3=-1.3333

P(Z=-1.3333)=0.091

=0.040(Approximate)