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 . Approximately 95% of the area under the normal curve is between
. Approximately 99.7% of the area under the normal curve is between
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
We find that the standardized value is 0.84162123
Hope these help!!