For a standard normal distribution, which of the following expressions must always be equal to 1?

P (z≤-a) - P (-a≤z≤a) + P (z≥a)

P (z≤-a) - P (-a≤z≤a) + P (z≥a)

P (z≤-a) + P (-a≤z≤a) - P (z≥a)

P (z≤-a) + P (-a≤z≤a) + P (Z≥a)

The correct answer is:

P (z≤-a) + P (-a≤z≤a) + P (Z≥a)

Explanation:

The probabilities in a z-table correspond with the area under the normal curve.

The first part of this answer, P (z≤-a), is the area to the left of the value - a under the curve.

The second part of this answer, P (-a≤z≤a), is the area under the curve from

-a to a.

The last part of this answer, P (Z≥a), is the area to the right of the value a under the curve.

Together, these three make up the entire normal curve. The entire area under the whole curve is 1; this means the sum of these three probabilities is 1.

For a standard normal distribution, the expression that is always equal to 1 is P (z≤-a) + P (-a≤z≤a) + P (Z≥a). This expression represents all of the possible values in a curve, or in other words, the total area of a curve. According to standard normal distribution, the total area of a curve is always equal to 1.