Math / Data & Statistics

QuestionDetermine the percent of data to the left of the $z$ -score: $z=1.44$ . 92.51\% 94.95\% 93.82\% 95.91\%

Studdy Solution

STEP 1

1. The $z$ -score represents the number of standard deviations a data point is from the mean in a standard normal distribution.
2. We are using the standard normal distribution table (or a calculator) to find the cumulative probability associated with a given $z$ -score.

STEP 2

1. Understand the concept of the $z$ -score and its relation to the standard normal distribution.
2. Use the standard normal distribution table or calculator to find the cumulative probability for $z = 1.44$ .
3. Interpret the cumulative probability as the percentage of data to the left of the $z$ -score.

STEP 3

Understand that a $z$ -score of 1.44 indicates that the data point is 1.44 standard deviations above the mean in a standard normal distribution.

STEP 4

Look up the cumulative probability for $z = 1.44$ in the standard normal distribution table or use a calculator. This value represents the area under the curve to the left of $z = 1.44$ .

STEP 5

The cumulative probability for $z = 1.44$ is approximately 0.9251.

STEP 6

Convert the cumulative probability to a percentage by multiplying by 100. Therefore, $0.9251 \times 100 = 92.51\%$ .
The percent of data to the left of the $z$ -score 1.44 is:
$\boxed{92.51\%}$

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QuestionDetermine the percent of data to the left of the $z$ -score: $z=1.44$ . 92.51\% 94.95\% 93.82\% 95.91\%

Studdy Solution

STEP 1

1. The $z$ -score represents the number of standard deviations a data point is from the mean in a standard normal distribution.
2. We are using the standard normal distribution table (or a calculator) to find the cumulative probability associated with a given $z$ -score.

STEP 2

STEP 3

Understand that a $z$ -score of 1.44 indicates that the data point is 1.44 standard deviations above the mean in a standard normal distribution.

STEP 4

Look up the cumulative probability for $z = 1.44$ in the standard normal distribution table or use a calculator. This value represents the area under the curve to the left of $z = 1.44$ .

STEP 5

The cumulative probability for $z = 1.44$ is approximately 0.9251.

STEP 6

Convert the cumulative probability to a percentage by multiplying by 100. Therefore, $0.9251 \times 100 = 92.51\%$ .
The percent of data to the left of the $z$ -score 1.44 is:
$\boxed{92.51\%}$

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QuestionDetermine the percent of data to the left of the zzz-score: z=1.44z=1.44z=1.44. 92.51\% 94.95\% 93.82\% 95.91\%

Studdy Solution

STEP 1

1. The z z z-score represents the number of standard deviations a data point is from the mean in a standard normal distribution.2. We are using the standard normal distribution table (or a calculator) to find the cumulative probability associated with a given z z z-score.

STEP 2

STEP 3

Understand that a z z z-score of 1.44 indicates that the data point is 1.44 standard deviations above the mean in a standard normal distribution.

STEP 4

Look up the cumulative probability for z=1.44 z = 1.44 z=1.44 in the standard normal distribution table or use a calculator. This value represents the area under the curve to the left of z=1.44 z = 1.44 z=1.44.

STEP 5

The cumulative probability for z=1.44 z = 1.44 z=1.44 is approximately 0.9251.

STEP 6

Convert the cumulative probability to a percentage by multiplying by 100. Therefore, 0.9251×100=92.51% 0.9251 \times 100 = 92.51\% 0.9251×100=92.51%. The percent of data to the left of the z z z-score 1.44 is:92.51% \boxed{92.51\%} 92.51%​

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QuestionDetermine the percent of data to the left of the $z$ -score: $z=1.44$ . 92.51\% 94.95\% 93.82\% 95.91\%

1. The $z$ -score represents the number of standard deviations a data point is from the mean in a standard normal distribution.
2. We are using the standard normal distribution table (or a calculator) to find the cumulative probability associated with a given $z$ -score.

Understand that a $z$ -score of 1.44 indicates that the data point is 1.44 standard deviations above the mean in a standard normal distribution.

Look up the cumulative probability for $z = 1.44$ in the standard normal distribution table or use a calculator. This value represents the area under the curve to the left of $z = 1.44$ .

The cumulative probability for $z = 1.44$ is approximately 0.9251.

Convert the cumulative probability to a percentage by multiplying by 100. Therefore, $0.9251 \times 100 = 92.51\%$ .
The percent of data to the left of the $z$ -score 1.44 is:
$\boxed{92.51\%}$