Questions: What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below. A. The mean and standard deviation have the values of μ=1 and σ=1. B. The mean and standard deviation have the values of μ=0 and σ=0. C. The mean and standard deviation have the values of μ=0 and σ=1. D. The mean and standard deviation have the values of μ=1 and σ=0.

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below. A. The mean and standard deviation have the values of μ=1 and σ=1. B. The mean and standard deviation have the values of μ=0 and σ=0. C. The mean and standard deviation have the values of μ=0 and σ=1. D. The mean and standard deviation have the values of μ=1 and σ=0.
Transcript text: What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below. A. The mean and standard deviation have the values of $\mu=1$ and $\sigma=1$. B. The mean and standard deviation have the values of $\mu=0$ and $\sigma=0$. C. The mean and standard deviation have the values of $\mu=0$ and $\sigma=1$. D. The mean and standard deviation have the values of $\mu=1$ and $\sigma=0$.
failed

Solution

failed
failed

Solution Steps

Step 1: Understanding the Standard Normal Distribution

A normal probability distribution is considered a standard normal distribution when its mean \( \mu \) and standard deviation \( \sigma \) are specifically defined as: \[ \mu = 0 \quad \text{and} \quad \sigma = 1 \]

Step 2: Calculating Z-scores

For the given range of \([-1, 1]\), we calculate the Z-scores: \[ Z_{start} = -1.0 \quad \text{and} \quad Z_{end} = 1.0 \]

Step 3: Calculating the Probability

The probability that the sample mean falls within the specified range is calculated using the cumulative distribution function \( \Phi \): \[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(1.0) - \Phi(-1.0) = 0.6827 \]

Final Answer

The correct answer to the question regarding the requirements for a normal probability distribution to be a standard normal probability distribution is: \[ \boxed{C. \text{The mean and standard deviation have the values of } \mu=0 \text{ and } \sigma=1.} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Simplify the rational expression. (2x^2 - 3x - 2) / (6x^3 + 3x^2 + 2x + 1)
failedAnswered
Solve the absolute value inequality. Graph the solution set. 1-2x-6<-1 Select the correct choice and, if necessary, fill in the answer box within your choice. A. The solution set in interval notation is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution is the empty set. Graph the solution set. Choose the correct answer. A. B. C. D. E. F.
failedAnswered
the measure of the missing angle.
failedAnswered
In which of the following situations is the probability calculated empirically? - A customer satisfaction survey reveals that 270 of the 300 respondents were satisfied with their service, so the estimated customer satisfaction rate is 90%. - A doctor believes that there is a 90% chance his patient will survive a procedure. - A professor has assigned a C grade to 10 of the first 25 exams she graded, so the estimated probability that the next exam will get a C is 40%. - Out of 1000 fans at a rock concert, 600 are male, so if a random person gets called to the stage, the probability that that person will be male is 60%. - A city with 100,000 people has 30,000 Caucasians, so the probability that a random person in this city is Caucasian is 30%.
failedAnswered
A certain chemical reaction releases 32.9 kJ / g of heat for each gram of reactant consumed. How can you calculate the heat produced by the consumption of 2.4 kg of reactant? Set the math up. But don't do any of it. Just leave your answer as a math expression. Also, be sure your answer includes all the correct unit symbols. heat =