Posted: May 8th, 2021

P9

Question 1

Given: Z ~ N(0,1)

Calculate – show all calculations

1.1P(- 2.25 <Z<2.52) = P(Z<2.52) – P(Z<-2.25) = 0.9941-0.0122 =

1.2P(Z>3.18)= 1- P(Z< 3.18) = 1-0.9993 =

1.3 = 1- P(Z< -2.5) =1-0.0062=

1.4 =

1.5= P(Z<2.58) – P(Z<0.38) = 0.9951 – 0.6380 =

1.6= P(Z<-1.25) – P(Z<-2.82) =0.1056-0.0024 =

1.7 =

1.8=>P(Z< ?) = 1-0.5319 =0.4681=P(Z< =-0.08)=> ? =

1.9=>P(Z< ?) = 1-0.6331 =0.3669=P(Z<-0.35)=> ? =

1.10= P(Z<0.068 ) => ? =

Question 2

A luxury passenger liner has 500 passengers on board whose ages are normally distributed around a mean of 60 years with a standard deviation of 12 years.

2.1 How many of the passengers are between 36 and 78 years old?

2.2What percentage of the passengers is between 56 and 66 years old?

2.3 =

2.4=

2.5What is the minimum age of the oldest 20% of passengers?

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