Answer:
[tex]P(0.25\le z\le 1.25)[/tex]
Step-by-step explanation:
Consider the probability table:
z Probability
0.00 0.5000
0.25 0.59871
0.50 0.6915
0.75 0.7734
1.00 0.8413
1.25 0.8944
1.50 0.9332
1.75 0.9599
We need to find the probability which is equal to approximately 0.2957.
[tex]P(-z)=1-P(z)[/tex]
[tex]P(-1.25)=1-P(1.25)[/tex]
[tex]P(-1.25)=1-0.8944[/tex]
[tex]P(-1.25)=0.1056[/tex]
The probability of P(-1.25) is 0.1056.
[tex]P(-1.25\le z\le 0.25)=P(0.25)-P(-1.25)[/tex]
[tex]P(-1.25\le z\le 0.25)=0.59871-0.1056=0.49311[/tex]
The probability of [tex]P(-1.25\le z\le 0.25)[/tex] is 0.49311.
[tex]P(-1.25\le z\le 0.75)=P(0.75)-P(-1.25)[/tex]
[tex]P(-1.25\le z\le 0.75)=0.7734-0.1056=0.6678[/tex]
The probability of [tex]P(-1.25\le z\le 0.75)[/tex] is 0.6678.
[tex]P(0.25\le z\le 1.25)=P(1.25)-P(0.25)[/tex]
[tex]P(0.25\le z\le 1.25)=0.8944-0.59871=0.29569[/tex]
The probability of [tex]P(0.25\le z\le 1.25)[/tex] is 0.29569.
[tex]P(0.75\le z\le 1.25)=P(1.25)-P(0.75)[/tex]
[tex]P(0.75\le z\le 1.25)=0.8944-0.7734=0.121[/tex]
The probability of [tex]P(0.75\le z\le 1.25)[/tex] is 0.121.
Therefore, the correct option is 3, i.e., [tex]P(0.25\le z\le 1.25)[/tex].
