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
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Explanation:

Step1: Recall the property of standard normal distribution

The standard normal distribution \(Z\sim N(0,1)\) is symmetric about \(z = 0\). That is, \(P(a<Z < b)=P(-b < Z<-a)\) for any real numbers \(a\) and \(b\) with \(a < b\).

Step2: Apply the symmetry property

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

Answer:

True