Math / Data & Statistics

QuestionUse 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. $P_{15}$
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The $z$ -score that corresponds to $\mathrm{P}_{15}$ is $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. The standard normal distribution table provides the area (probability) to the left of a given z-score.
2. $P_{15}$ refers to the 15th percentile, meaning the area to the left of the z-score is 0.15.
3. If the exact area is not in the table, use the closest value.
4. If the area is halfway between two entries, use the average of the corresponding z-scores.

STEP 2

1. Locate the area in the standard normal table.
2. Determine the corresponding z-score.
3. Handle cases where the area is not directly in the table.

STEP 3

Locate the area 0.15 in the standard normal table.

STEP 4

Search for the closest value to 0.15 in the table.

STEP 5

Identify the z-score corresponding to the closest area. If the area is exactly halfway between two values, calculate the average z-score.

STEP 6

Using the standard normal table, the closest area to 0.15 is 0.1492, which corresponds to a z-score of approximately -1.04.

STEP 7

Since 0.15 is not exactly halfway between two entries, use the z-score corresponding to the closest area.
The z-score that corresponds to $P_{15}$ is:
$\boxed{-1.04}$

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Studdy Solution

STEP 1

STEP 2

1. Locate the area in the standard normal table.
2. Determine the corresponding z-score.
3. Handle cases where the area is not directly in the table.

STEP 3

Locate the area 0.15 in the standard normal table.

STEP 4

Search for the closest value to 0.15 in the table.

STEP 5

Identify the z-score corresponding to the closest area. If the area is exactly halfway between two values, calculate the average z-score.

STEP 6

Using the standard normal table, the closest area to 0.15 is 0.1492, which corresponds to a z-score of approximately -1.04.

STEP 7

Since 0.15 is not exactly halfway between two entries, use the z-score corresponding to the closest area.
The z-score that corresponds to $P_{15}$ is:
$\boxed{-1.04}$

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Studdy Solution

STEP 1

STEP 2

1. Locate the area in the standard normal table.2. Determine the corresponding z-score.3. Handle cases where the area is not directly in the table.

STEP 3

Locate the area 0.15 in the standard normal table.

STEP 4

Search for the closest value to 0.15 in the table.

STEP 5

Identify the z-score corresponding to the closest area. If the area is exactly halfway between two values, calculate the average z-score.

STEP 6

Using the standard normal table, the closest area to 0.15 is 0.1492, which corresponds to a z-score of approximately -1.04.

STEP 7

Since 0.15 is not exactly halfway between two entries, use the z-score corresponding to the closest area. The z-score that corresponds to P15 P_{15} P15​ is:−1.04 \boxed{-1.04} −1.04​

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1. Locate the area in the standard normal table.
2. Determine the corresponding z-score.
3. Handle cases where the area is not directly in the table.

Since 0.15 is not exactly halfway between two entries, use the z-score corresponding to the closest area.
The z-score that corresponds to $P_{15}$ is:
$\boxed{-1.04}$