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Questions:

1. random variable X normally distributed with mean 25.

The shaded region between 25 and 27 represents 30% of the distribution.

a). Find P(X>27)

b). Find the standard deviation of X

2. A random variable X is distributed normally with a mean of 20 and variance 9.

a). Find P(X<(or equal to)24.5)

b). Let P(X<(or equal to)k)=0.85

ii). Find the value of k.

So lost atm, tried so many different ways but I'm getting wrong answers- please help.

1. random variable X normally distributed with mean 25.

The shaded region between 25 and 27 represents 30% of the distribution.

a). Find P(X>27)

b). Find the standard deviation of X

2. A random variable X is distributed normally with a mean of 20 and variance 9.

a). Find P(X<(or equal to)24.5)

b). Let P(X<(or equal to)k)=0.85

ii). Find the value of k.

So lost atm, tried so many different ways but I'm getting wrong answers- please help.

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

IB Mathematics SL Normal Distribution

Answers:

1. random variable X normally distributed with mean 25.

The shaded region between 25 and 27 represents 30% of the distribution.

a). Find P(X>27)

Answer:

b). Find the standard deviation of X

Answer:

Let the random variable X , so that

We know that

Since we don’t know the standard deviation of X, we cannot use the inverse normal. Therefore we have to transform the random variable to that of

, using the transformation

we have the following

Using GDC Casio fx-9860G SD

MAIN MENU > STAT>DIST(F5)>NORM(F1)>InvN>

Setting Tail: right

Area: 0.2

:1

:0

We find that the standardized value is 0.8416

Therefore

2. A random variable X is distributed normally with a mean of 20 and variance 9.

a). Find P(X<(or equal to)24.5)

Answer:

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:24.5, , and you get

b). Let P(X<(or equal to)k)=0.85

ii). Find the value of k.

Answer:

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Left, Area:0.85, , and you get

Hope these Help!!

Answers:

1. random variable X normally distributed with mean 25.

The shaded region between 25 and 27 represents 30% of the distribution.

a). Find P(X>27)

Answer:

b). Find the standard deviation of X

Answer:

Let the random variable X , so that

We know that

Since we don’t know the standard deviation of X, we cannot use the inverse normal. Therefore we have to transform the random variable to that of

, using the transformation

we have the following

Using GDC Casio fx-9860G SD

MAIN MENU > STAT>DIST(F5)>NORM(F1)>InvN>

Setting Tail: right

Area: 0.2

:1

:0

We find that the standardized value is 0.8416

Therefore

2. A random variable X is distributed normally with a mean of 20 and variance 9.

a). Find P(X<(or equal to)24.5)

Answer:

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:24.5, , and you get

b). Let P(X<(or equal to)k)=0.85

ii). Find the value of k.

Answer:

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Left, Area:0.85, , and you get

Hope these Help!!

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

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