Math / Data & Statistics

QuestionFind the z-score that has $3.533 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. We are working with a standard normal distribution, which has a mean of 0 and a standard deviation of 1.
2. The z-score corresponds to the cumulative probability (area to the left under the curve).

STEP 2

1. Understand the relationship between z-scores and cumulative probabilities.
2. Use statistical tables or software to find the z-score for the given cumulative probability.

STEP 3

Understand that the z-score is a measure of how many standard deviations an element is from the mean. The cumulative probability given is $3.533\%$ , which is equivalent to $0.03533$ in decimal form.

STEP 4

Use a z-table, calculator, or statistical software to find the z-score corresponding to a cumulative probability of $0.03533$ .

STEP 5

Look up the cumulative probability $0.03533$ in the z-table or use software to find the z-score. The closest cumulative probability in standard z-tables is typically found between two values. For $0.03533$ , the z-score is approximately $-1.81$ .
The z-score is:
$\boxed{-1.81}$

Was this helpful?

QuestionFind the z-score that has $3.533 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. We are working with a standard normal distribution, which has a mean of 0 and a standard deviation of 1.
2. The z-score corresponds to the cumulative probability (area to the left under the curve).

STEP 2

1. Understand the relationship between z-scores and cumulative probabilities.
2. Use statistical tables or software to find the z-score for the given cumulative probability.

STEP 3

Understand that the z-score is a measure of how many standard deviations an element is from the mean. The cumulative probability given is $3.533\%$ , which is equivalent to $0.03533$ in decimal form.

STEP 4

Use a z-table, calculator, or statistical software to find the z-score corresponding to a cumulative probability of $0.03533$ .

STEP 5

Look up the cumulative probability $0.03533$ in the z-table or use software to find the z-score. The closest cumulative probability in standard z-tables is typically found between two values. For $0.03533$ , the z-score is approximately $-1.81$ .
The z-score is:
$\boxed{-1.81}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the z-score that has 3.533%3.533 \%3.533% of the distribution's area to its left.The z-score is □\square□ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. We are working with a standard normal distribution, which has a mean of 0 and a standard deviation of 1.2. The z-score corresponds to the cumulative probability (area to the left under the curve).

STEP 2

1. Understand the relationship between z-scores and cumulative probabilities.2. Use statistical tables or software to find the z-score for the given cumulative probability.

STEP 3

Understand that the z-score is a measure of how many standard deviations an element is from the mean. The cumulative probability given is 3.533%3.533\%3.533%, which is equivalent to 0.035330.035330.03533 in decimal form.

STEP 4

Use a z-table, calculator, or statistical software to find the z-score corresponding to a cumulative probability of 0.035330.035330.03533.

STEP 5

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the z-score that has $3.533 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

1. We are working with a standard normal distribution, which has a mean of 0 and a standard deviation of 1.
2. The z-score corresponds to the cumulative probability (area to the left under the curve).

1. Understand the relationship between z-scores and cumulative probabilities.
2. Use statistical tables or software to find the z-score for the given cumulative probability.

Understand that the z-score is a measure of how many standard deviations an element is from the mean. The cumulative probability given is $3.533\%$ , which is equivalent to $0.03533$ in decimal form.

Use a z-table, calculator, or statistical software to find the z-score corresponding to a cumulative probability of $0.03533$ .