Respuesta :
A z-table is also known as the standard normal distribution table. The probability of P(0.75≤ z ≤ 1.25) is 0.121.
What is a Z-table?
A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
As it is given that the probability and the z-table is given to us, as shown below,
 z      Probability
0.00 Â Â Â 0.5000
0.25 Â Â Â 0.59871
0.50 Â Â Â Â 0.6915
0.75 Â Â Â Â 0.7734
1.00 Â Â Â Â 0.8413
1.25 Â Â Â Â 0.8944
1.50 Â Â Â Â Â 0.9332
1.75 Â Â Â Â Â 0.9599
The following probabilities can be written as:
1. Â The probability of P(-1.25)
[tex]P(-z)=1-P(z)\\\\P(-1.25)=1-P(1.25)\\\\P(-1.25)=1-(0.8944)\\\\P(-1.25)=0.1056[/tex]
The probability of P(-1.25) is 0.1056.
2.  The probability of P(-1.25 ≤ z ≤ 0.25)
[tex]P(-1.25\leq z\leq 0.25)=P(0.25)-P(-1.25)\\\\P(-1.25\leq z\leq 0.25)=0.59871-0.1056=0.49311[/tex]
The probability of P(-1.25 ≤ z ≤ 0.25) is 0.49311.
3.  The probability of P(-1.25 ≤ z ≤ 0.75)
[tex]P(-1.25\leq z\leq 0.75)=P(0.75)-P(-1.25)\\\\P(-1.25\leq z\leq 0.75)=0.7734-0.1056=0.6678[/tex]
The probability of P(-1.25 ≤ z ≤ 0.75) is 0.6678.
4.  The probability of P(0.25 ≤ z ≤ 1.25)
[tex]P(0.25 \leq z\leq 1.25)=P(1.25)-P(0.25)\\\\P(0.25\leq z\leq 1.25)=0.8944-0.59871=0.29569[/tex]
The probability of P(0.25 ≤ z ≤ 1.25) is 0.29569.
5.  The probability of P(0.75≤ z ≤ 1.25)
[tex]P(0.75\leq z\leq 1.25)=P(1.25)-P(0.75)\\\\P(0.75\leq z\leq 1.25)=0.8944-0.7734=0.121[/tex]
The probability of P(0.75≤ z ≤ 1.25) is 0.121.
Learn more about Z-table:
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