Question

Which of the following statements is equivalent to P (z greater-than-or-equal-to 1. 7)? P (z greater-than-or-equal-to negative 1. 7) 1 minus P (z greater-than-or-equal-to negative 1. 7) P (z less-than-or-equal-to 1. 7) 1 minus P (z less-than-or-equal-to 1. 7).

Answer 1

This $\rm P(Z\geq 1.7)$  is equivalent to  $\rm 1-P(Z\leq 1.7)$

It is given that the  $\rm P(Z\geq 1.7)$

It is required to find which statement is equivalent to $\rm P(Z\geq 1.7)$

The statements are:

$a) \ \rm P(Z\geq -1.7)\\b) \ \rm 1-P(Z\geq -1.7)\\c) \ \rm P(Z\leq 1.7)\\d) \ \rm 1-P(Z\leq 1.7)$

What is a normal distribution?

It is defined as the continuous distribution probability curve which is most likely symmetric around the mean. At Z=0, the probability is 50-50% on the Z curve. It is also called a bell-shaped curve.

We have the $\rm P(Z\geq 1.7)$

We know that:

$\rm P(Z\leq a)=P(Z\geq -a)\\\rm P(Z\geq a)=P(Z\leq -a)$

If we compare statement (a) and statement (c), we will see these options are not equivalent to  $\rm P(Z\geq 1.7)$

For statement (b) if we plot the graph for the given statement we will get the negative area of the bell curve hence it is also incorrect.

For statement (d) if we plot the graph for the given statement we will get the positive area which is equivalent to the $\rm P(Z\geq 1.7)$

Thus, the $\rm P(Z\geq 1.7)$  is equivalent to  $\rm 1-P(Z\leq 1.7)$

Know more about the normal distribution here:

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