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Which of the following statements is equivalent to [tex]\(P(z \geq 1.7)\)[/tex]?

A. [tex]\(P(z \geq -1.7)\)[/tex]
B. [tex]\(1 - P(z \geq -1.7)\)[/tex]
C. [tex]\(P(z \leq 1.7)\)[/tex]
D. [tex]\(1 - P(z \geq 1.7)\)[/tex]

Sagot :

GinnyAnsweridn
To determine which statement is equivalent to [tex]\( P(z \geq 1.7) \)[/tex], let's break down what each option represents in terms of standard normal distribution probabilities.

1. [tex]\( P(z \geq -1.7) \)[/tex]
- This represents the probability that the standard normal variable [tex]\( z \)[/tex] is greater than or equal to -1.7. This is not equivalent to [tex]\( P(z \geq 1.7) \)[/tex], so this option is incorrect.

2. [tex]\( 1 - P(z \geq -1.7) \)[/tex]
- This is the complement of the probability that [tex]\( z \)[/tex] is greater than or equal to -1.7. This is not equivalent to [tex]\( P(z \geq 1.7) \)[/tex], so this option is incorrect.

3. [tex]\( P(z \leq 1.7) \)[/tex]
- This represents the probability that the standard normal variable [tex]\( z \)[/tex] is less than or equal to 1.7. The relationship between [tex]\( P(z \geq 1.7) \)[/tex] and [tex]\( P(z \leq 1.7) \)[/tex] uses the fact that the total probability under the normal distribution curve sums to 1. Thus, [tex]\( P(z \geq 1.7) = 1 - P(z \leq 1.7) \)[/tex]. This means this option is also not equivalent to [tex]\( P(z \geq 1.7) \)[/tex].

4. [tex]\( 1 - P(z \geq 1.7) \)[/tex]
- This is the complement of [tex]\( P(z \geq 1.7) \)[/tex]. Since we are looking for the original expression [tex]\( P(z \geq 1.7) \)[/tex], this option is incorrect.

From the given options, none of them directly match [tex]\( P(z \geq 1.7) \)[/tex]. However, if we consider the relationships:
- [tex]\( P(z \geq 1.7) = 1 - P(z \leq 1.7) \)[/tex]

The closest match to express [tex]\( P(z \geq 1.7) \)[/tex] indirectly would be using the relationship that [tex]\( 1 - P(z \leq 1.7) \)[/tex] can represent [tex]\( P(z \geq 1.7) \)[/tex].

Therefore, none of the statements provided are exactly the correct equivalent of [tex]\( P(z \geq 1.7) \)[/tex], but by understanding the probability relationships, [tex]\( P(z \leq 1.7) \)[/tex] helps form the equivalent statement:
[tex]\[ P(z \geq 1.7) = 1 - P(z \leq 1.7) \][/tex]

Hence, the equivalent and correct understanding relates back to:
[tex]\[ \boxed{1} \][/tex]
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