The given information "z-score for the first quartile and the third quartile of the standard normal distribution."

We know that 0.250 square unit of the area covered in the standard normal distribution to the left of the third quartile.

We have to find the z-score that has an area of 0.250 square units to the left of the z-score.

So from the table of standard normal distribution we get the z-score of the area 0.250 square unit as \(z = 0.67\)

And 0.250 square unit of the area covered in the standard normal distribution to the right of the first quartile.

We have to find the z-score that has an area of 0.250 square units to

the right of the z-score.

So from the table of standard normal distribution we get the z-score of the area 0.250 square unit as \(z = 0.67\)

Since the z-score of the first quartile lies to left of 0, thus the z-score of first quartile is \(z = -0.67\)

We know that 0.250 square unit of the area covered in the standard normal distribution to the left of the third quartile.

We have to find the z-score that has an area of 0.250 square units to the left of the z-score.

So from the table of standard normal distribution we get the z-score of the area 0.250 square unit as \(z = 0.67\)

And 0.250 square unit of the area covered in the standard normal distribution to the right of the first quartile.

We have to find the z-score that has an area of 0.250 square units to

the right of the z-score.

So from the table of standard normal distribution we get the z-score of the area 0.250 square unit as \(z = 0.67\)

Since the z-score of the first quartile lies to left of 0, thus the z-score of first quartile is \(z = -0.67\)