Use the standard normal table to find the z-score that corresponds to the given

Question

Use the standard normal table to find the z-score that corresponds to the given percentile. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score.

P2

Use the standard normal table to find the z-score that corresponds to the cumulative area.0053. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores.

Find the z-scores for which 85% of the distribution's area lies between minusz and z. The z-scores are ( )

Explanation / Answer

Solution :

The z-scores for which 85% of the distribution's area lies between minusz and z are

P(-z < Z < z) = 85 %

P( Z < z) - P(Z < -z) = 0.85

2P(Z < z) - 1 = 0.85

2P(Z < z) = 1 + 0.85 = 1.85

P(Z < z) = 1.85 / 2 = 0.925

P(Z < z) = 0.925

P(Z < 1.44) = 0.925

P(-1.44 < Z < 1.44) = 85 %

The z-scores for which 85% of the distribution's area lies between minusz and z .

The Z-scores are (-1.44 , 1.44) .

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