QuestionCalculate the probability $\mathrm{P}(0.58<\mathrm{z}<1.74)$ for a Standard Normal Random Variable using the provided tables.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a standard normal random variable, which means the mean is0 and the standard deviation is1. . We are asked to calculate the probability that the variable is between0.58 and1.74.
3. We have access to a standard normal distribution table.

STEP 2

The standard normal distribution table gives the probability that a standard normal random variable is less than a given value. So, to find the probability that the variable is between0.58 and1.74, we need to calculate the probability that the variable is less than1.74 and then subtract the probability that it is less than0.58.
$(0.58<z<1.74) =(z<1.74) -(z<0.58)$

STEP 3

Now, we need to look up the probabilities $(z<1.74)$ and $(z<0.58)$ in the standard normal distribution table.

STEP 4

From the standard normal distribution table, we find that $(z<1.74)$ is approximately0.9591 and $(z<0.58)$ is approximately0.7197.

STEP 5

Now, we can plug these values back into our equation from2 to find the probability that the variable is between0.58 and1.74.
$(0.58<z<1.74) =(z<1.74) -(z<0.58) =0.9591 -0.7197$

STEP 6

Calculate the probability.
$(0.58<z<1.74) =0.9591 -0.719 =0.2394$ The probability that a standard normal random variable is between0.58 and1.74 is approximately0.2394.

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QuestionCalculate the probability $\mathrm{P}(0.58<\mathrm{z}<1.74)$ for a Standard Normal Random Variable using the provided tables.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a standard normal random variable, which means the mean is0 and the standard deviation is1. . We are asked to calculate the probability that the variable is between0.58 and1.74.
3. We have access to a standard normal distribution table.

STEP 2

STEP 3

Now, we need to look up the probabilities $(z<1.74)$ and $(z<0.58)$ in the standard normal distribution table.

STEP 4

From the standard normal distribution table, we find that $(z<1.74)$ is approximately0.9591 and $(z<0.58)$ is approximately0.7197.

STEP 5

Now, we can plug these values back into our equation from2 to find the probability that the variable is between0.58 and1.74.
$(0.58<z<1.74) =(z<1.74) -(z<0.58) =0.9591 -0.7197$

STEP 6

Calculate the probability.
$(0.58<z<1.74) =0.9591 -0.719 =0.2394$ The probability that a standard normal random variable is between0.58 and1.74 is approximately0.2394.

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QuestionCalculate the probability P(0.58<z<1.74)\mathrm{P}(0.58<\mathrm{z}<1.74)P(0.58<z<1.74) for a Standard Normal Random Variable using the provided tables.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a standard normal random variable, which means the mean is0 and the standard deviation is1. . We are asked to calculate the probability that the variable is between0.58 and1.74.3. We have access to a standard normal distribution table.

STEP 2

STEP 3

Now, we need to look up the probabilities (z<1.74)(z<1.74)(z<1.74) and (z<0.58)(z<0.58)(z<0.58) in the standard normal distribution table.

STEP 4

From the standard normal distribution table, we find that (z<1.74)(z<1.74)(z<1.74) is approximately0.9591 and (z<0.58)(z<0.58)(z<0.58) is approximately0.7197.

STEP 5

Now, we can plug these values back into our equation from2 to find the probability that the variable is between0.58 and1.74.(0.58<z<1.74)=(z<1.74)−(z<0.58)=0.9591−0.7197(0.58<z<1.74) =(z<1.74) -(z<0.58) =0.9591 -0.7197(0.58<z<1.74)=(z<1.74)−(z<0.58)=0.9591−0.7197

STEP 6

Calculate the probability.(0.58<z<1.74)=0.9591−0.719=0.2394(0.58<z<1.74) =0.9591 -0.719 =0.2394(0.58<z<1.74)=0.9591−0.719=0.2394The probability that a standard normal random variable is between0.58 and1.74 is approximately0.2394.

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

QuestionCalculate the probability $\mathrm{P}(0.58<\mathrm{z}<1.74)$ for a Standard Normal Random Variable using the provided tables.

Assumptions1. We are dealing with a standard normal random variable, which means the mean is0 and the standard deviation is1. . We are asked to calculate the probability that the variable is between0.58 and1.74.
3. We have access to a standard normal distribution table.

Now, we need to look up the probabilities $(z<1.74)$ and $(z<0.58)$ in the standard normal distribution table.

From the standard normal distribution table, we find that $(z<1.74)$ is approximately0.9591 and $(z<0.58)$ is approximately0.7197.

Now, we can plug these values back into our equation from2 to find the probability that the variable is between0.58 and1.74.
$(0.58<z<1.74) =(z<1.74) -(z<0.58) =0.9591 -0.7197$

Calculate the probability.
$(0.58<z<1.74) =0.9591 -0.719 =0.2394$ The probability that a standard normal random variable is between0.58 and1.74 is approximately0.2394.