QuestionFind the proportion of scores in a $\mathrm{z}$ distribution between $\mathrm{z} = -2.00$ and $\mathrm{z} = 0.00$ .

Studdy Solution

STEP 1

Assumptions1. We are dealing with a standard normal distribution (z distribution), which has a mean of0 and a standard deviation of1. . We are asked to find the proportion of scores that fall between a z score of -.00 and a z score of0.00.

STEP 2

In a standard normal distribution, the total area under the curve is1 (or100%). The area under the curve between any two points corresponds to the probability of a score falling between those two values.

STEP 3

The z score of0.00 corresponds to the mean of the distribution. Therefore, the area under the curve to the left of the mean is0.5 (or50%).

STEP 4

To find the proportion of scores between a z score of -2.00 and a z score of0.00, we need to find the area under the curve to the left of the z score of -2.00 and subtract it from0..

STEP 5

The area to the left of a z score of -2.00 can be found using a standard normal distribution table or a z score calculator. According to the standard normal distribution table, the area to the left of a z score of -2.00 is approximately0.0228.

STEP 6

Subtract the area to the left of a z score of -2.00 from0.5 to find the proportion of scores between a z score of -2.00 and a z score of0.00.
$Proportion =0.5 -0.0228$

STEP 7

Calculate the proportion.
$Proportion =0.5 -0.022 =0.4772$ So, the proportion of scores on a z distribution that fall between a z score of -2.00 and a z score of0.00 is0.4772.

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QuestionFind the proportion of scores in a $\mathrm{z}$ distribution between $\mathrm{z} = -2.00$ and $\mathrm{z} = 0.00$ .

Studdy Solution

STEP 1

Assumptions1. We are dealing with a standard normal distribution (z distribution), which has a mean of0 and a standard deviation of1. . We are asked to find the proportion of scores that fall between a z score of -.00 and a z score of0.00.

STEP 2

In a standard normal distribution, the total area under the curve is1 (or100%). The area under the curve between any two points corresponds to the probability of a score falling between those two values.

STEP 3

The z score of0.00 corresponds to the mean of the distribution. Therefore, the area under the curve to the left of the mean is0.5 (or50%).

STEP 4

To find the proportion of scores between a z score of -2.00 and a z score of0.00, we need to find the area under the curve to the left of the z score of -2.00 and subtract it from0..

STEP 5

The area to the left of a z score of -2.00 can be found using a standard normal distribution table or a z score calculator. According to the standard normal distribution table, the area to the left of a z score of -2.00 is approximately0.0228.

STEP 6

Subtract the area to the left of a z score of -2.00 from0.5 to find the proportion of scores between a z score of -2.00 and a z score of0.00.
$Proportion =0.5 -0.0228$

STEP 7

Calculate the proportion.
$Proportion =0.5 -0.022 =0.4772$ So, the proportion of scores on a z distribution that fall between a z score of -2.00 and a z score of0.00 is0.4772.

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QuestionFind the proportion of scores in a z\mathrm{z}z distribution between z=−2.00\mathrm{z} = -2.00z=−2.00 and z=0.00\mathrm{z} = 0.00z=0.00.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a standard normal distribution (z distribution), which has a mean of0 and a standard deviation of1. . We are asked to find the proportion of scores that fall between a z score of -.00 and a z score of0.00.

STEP 2

In a standard normal distribution, the total area under the curve is1 (or100%). The area under the curve between any two points corresponds to the probability of a score falling between those two values.

STEP 3

The z score of0.00 corresponds to the mean of the distribution. Therefore, the area under the curve to the left of the mean is0.5 (or50%).

STEP 4

To find the proportion of scores between a z score of -2.00 and a z score of0.00, we need to find the area under the curve to the left of the z score of -2.00 and subtract it from0..

STEP 5

The area to the left of a z score of -2.00 can be found using a standard normal distribution table or a z score calculator. According to the standard normal distribution table, the area to the left of a z score of -2.00 is approximately0.0228.

STEP 6

Subtract the area to the left of a z score of -2.00 from0.5 to find the proportion of scores between a z score of -2.00 and a z score of0.00.Proportion=0.5−0.0228Proportion =0.5 -0.0228Proportion=0.5−0.0228

STEP 7

Calculate the proportion.Proportion=0.5−0.022=0.4772Proportion =0.5 -0.022 =0.4772Proportion=0.5−0.022=0.4772So, the proportion of scores on a z distribution that fall between a z score of -2.00 and a z score of0.00 is0.4772.

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

QuestionFind the proportion of scores in a $\mathrm{z}$ distribution between $\mathrm{z} = -2.00$ and $\mathrm{z} = 0.00$ .

Subtract the area to the left of a z score of -2.00 from0.5 to find the proportion of scores between a z score of -2.00 and a z score of0.00.
$Proportion =0.5 -0.0228$

Calculate the proportion.
$Proportion =0.5 -0.022 =0.4772$ So, the proportion of scores on a z distribution that fall between a z score of -2.00 and a z score of0.00 is0.4772.