Which of the following probabilities is equal to approximately 0.2957? use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.25 0.5987 0.50 0.6915 0.75 0.7734 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599 p (negative 1.25 less-than-or-equal-to z less-than-or-equal-to 0.25) p (negative 1.25 less-than-or-equal-to z less-than-or-equal-to 0.75) p (0.25 less-than-or-equal-to z less-than-or-equal-to 1.25) p (0.75 less-than-or-equal-to z less-than-or-equal-to 1.25)

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 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

The following probabilities can be written as:

1. 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:

https://brainly.com/question/6096474