Question

question 9
true or false: the probability that a standard normal variable, z, is between 2.70 and 2.10 is the same as the probability z is between -2.10 and -2.70.
true
false

Explanation:

Step1: Use the property of standard normal distribution

The standard normal distribution is symmetric about \(z = 0\). That is, \(P(a<Z < b)=P(-b < Z<-a)\)

Let \(a = 2.10\) and \(b=2.70\). Then \(P(2.10 < Z < 2.70)=P(- 2.70<Z<-2.10)\)

Step2: Analyze the given probability statement

The probability that \(Z\) is between \(2.70\) and \(2.10\) (i.e., \(P(2.10 < Z < 2.70)\)) and the probability that \(Z\) is between \(-2.10\) and \(-2.70\) (i.e., \(P(-2.70 < Z<-2.10)\)) are equal due to the symmetry of the standard - normal distribution.

Answer:

True