The first forum for Mathematics compatible also with ib mathematics (HL,SL,studies,myp mathematics) - ib math Revision Notes

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Questions:

1. A random variable X is distributed normally with mean 450 and standard deviation 20.

a). Find P(X<(or equal to)475)

b). Given that P(X>a)=0.27, find a.

2. The heights of certain plants are normally distributed. The plants are classified into three categories.

The shortest 12.92% are in category A.

The tallest 10.38% are in category C.

All the other plants are in category B with heights between r cm and t cm.

a). Diagram to represent this info.

b). Given that the mean height is 6.84 cm and the standard deviation 0.25cm, find the value of r and t

1. A random variable X is distributed normally with mean 450 and standard deviation 20.

a). Find P(X<(or equal to)475)

b). Given that P(X>a)=0.27, find a.

2. The heights of certain plants are normally distributed. The plants are classified into three categories.

The shortest 12.92% are in category A.

The tallest 10.38% are in category C.

All the other plants are in category B with heights between r cm and t cm.

a). Diagram to represent this info.

b). Given that the mean height is 6.84 cm and the standard deviation 0.25cm, find the value of r and t

- judIB
**Posts:**0**Joined:**Sun Jul 07, 2013 5:50 pm

IB Math SL Normal Distribution

Answers:

1. A random variable X is distributed normally with mean 450 and standard deviation 20.

a). Find P(X<(or equal to)475)

Answer:

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:475, , and you get

b). Given that P(X>a)=0.27, find a.

Answer:

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Right, Area:0.27, , and you get

a=462.25626

2. The heights of certain plants are normally distributed. The plants are classified into three categories.

The shortest 12.92% are in category A.

The tallest 10.38% are in category C.

All the other plants are in category B with heights between r cm and t cm.

a). Diagram to represent this info.

b). Given that the mean height is 6.84 cm and the standard deviation 0.25cm, find the value of r and t

Answer:

P(q<B<r)=0.9

Again you have an inverse normal case with Area 100%-12.92%-10.38%=76.7%

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Central, Area:0.767, , and you get

q=6.5418337 and r=7.13816663

Hope these help!!

Answers:

1. A random variable X is distributed normally with mean 450 and standard deviation 20.

a). Find P(X<(or equal to)475)

Answer:

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:475, , and you get

b). Given that P(X>a)=0.27, find a.

Answer:

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Right, Area:0.27, , and you get

a=462.25626

2. The heights of certain plants are normally distributed. The plants are classified into three categories.

The shortest 12.92% are in category A.

The tallest 10.38% are in category C.

All the other plants are in category B with heights between r cm and t cm.

a). Diagram to represent this info.

b). Given that the mean height is 6.84 cm and the standard deviation 0.25cm, find the value of r and t

Answer:

P(q<B<r)=0.9

Again you have an inverse normal case with Area 100%-12.92%-10.38%=76.7%

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Central, Area:0.767, , and you get

q=6.5418337 and r=7.13816663

Hope these help!!

- miranda
**Posts:**268**Joined:**Mon Jan 28, 2013 8:03 pm

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