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IB Mathematics HL – Continuous Probability Distribution, Normal Distribution

How can we find the standard deviation of the weight of a population of dogs which is found to be normally distributed with mean 7.4 Kg and the 20% of the dogs weigh at least 8 Kg.

Thanks

How can we find the standard deviation of the weight of a population of dogs which is found to be normally distributed with mean 7.4 Kg and the 20% of the dogs weigh at least 8 Kg.

Thanks

- elizabeth
**Posts:**0**Joined:**Mon Jan 28, 2013 8:09 pm

IB Mathematics HL – Continuous Probability Distribution, Normal Distribution

A normal distribution is a continuous probability distribution for a random variable X. The graph of a normal distribution is called the normal curve. A normal distribution has the following properties.

1. The mean, median, and mode are equal.

2. The normal curve is bell shaped and is symmetric about the mean.

3. The total are under the normal curve is equal to one.

4. The normal curve approaches, but never touches, the x-axis as it extends farther and farther away from the mean.

Approximately 68% of the area under the normal curve is between and

and . Approximately 95% of the area under the normal curve is between and . Approximately 99.7% of the area under the normal curve is between and

The standard normal distribution is a normal probability distribution that has a mean of 0 and a standard deviation of 1.

Concerning your question

Let the random variable W denote the weight of the dogs, so that

We know that

Since we don’t know the standard deviation, 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 0.84162123

Therefore

Hope these help!!

A normal distribution is a continuous probability distribution for a random variable X. The graph of a normal distribution is called the normal curve. A normal distribution has the following properties.

1. The mean, median, and mode are equal.

2. The normal curve is bell shaped and is symmetric about the mean.

3. The total are under the normal curve is equal to one.

4. The normal curve approaches, but never touches, the x-axis as it extends farther and farther away from the mean.

Approximately 68% of the area under the normal curve is between and

and . Approximately 95% of the area under the normal curve is between and . Approximately 99.7% of the area under the normal curve is between and

The standard normal distribution is a normal probability distribution that has a mean of 0 and a standard deviation of 1.

Concerning your question

Let the random variable W denote the weight of the dogs, so that

We know that

Since we don’t know the standard deviation, 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 0.84162123

Therefore

Hope these help!!

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

Thank you miranda!!

- elizabeth
**Posts:**0**Joined:**Mon Jan 28, 2013 8:09 pm

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