Question

If you know that the probability that a normal variable exceeds a certain number Q, is .10, you can be sure that the probability that this variable is less than -Q

Answer 1

solution:

Normal distribution: It is a probability distribution that is symmetric about mean,showing that data near the     mean are more frequent in occurrence than the data far from the mean . It is also known as "Gaussian Distribution".

The following are the properties of normal distribution

  

---> The distribution of curve is symmetric about mean and it is bell shaped curve.

---> The mean , median and mode are equal and coincide at centre

---> The area under the curve is 1

since the data is symmetric about its mean () with standard deviation ()

For a certain number k , P(X<k) = P(X>-k)

Let X be the normal random variable

Given that

Probability that variable exceeds a certain number Q = P(X>Q) = 0.10

Then, P(X<-Q) = 0.10 [ The data is symmetric ]

Therefore, you can be sure that the probability that this variable is less than -Q is 0.10