Question

For a standard normal distribution, if P (z less-than-or-equal-to a) = 0. 7116, what is the value of P (z greater-than-or-equal-to a)? 0. 2116 0. 2884 0. 7116 0. 7884.

Answer 1

For the standard normal distribution, if P (z≤a) = 0. 7116, then the value of P(z≥a) is 0.2884.

What is Standard normal distribution?

The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1.

As it is given that the value of P(z≤a)=0.7116, therefore, for P(z≤a) we can write,

$P(z\leq a) = 0.7116\\\\P(z > a) =1- 0.7116$

But as we know the fact that in continuous distribution, the probability of a single point is 0, therefore, we can write

$P(Z \leq z) = P(Z < z) )$

Similarly, for P(z>a)=0.7116 we can write,

$P(z > a) = 1-0.7116\\\\P(z \geq a) = 1-0.7116\\\\P(z \geq a) = P(z=a) + P(z > a) = 1- 0+0.7116\\\\P(z \geq a) = 0.2884$

Hence, For the standard normal distribution, if P (z≤a) = 0. 7116, then the value of P (z≥a) is 0.2884.

Learn more about Standard normal distribution:

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