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What is the area under the standard normal distribution curve between z0.75 and z1.89?
0.1972
Why does a researcher want to go from a normal distribution to a standard normal distributio?
A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.
What is The area under the normal curve to the right of mu and mu equals?
In a standard normal distribution, the area under the curve to the right of the mean (mu) is 0.5. This is because the normal distribution is symmetric around the mean, and half of the total area (which equals 1) lies to the right of the mean and half to the left. Therefore, for any normal distribution where mu is the mean, the area to the right of mu is always 0.5.
Why is only one normal table need to find any probability under the normal curve?
A normal distribution is defined by its mean and standard deviation, which are sufficient to describe the entire curve. Once you know these two parameters, you can use the standard normal table (Z-table) to find probabilities for any normal distribution by standardizing values. This process involves converting any normal variable to a standard score (Z-score), which allows you to utilize the same table for all normal distributions. Therefore, only one normal table is needed for any probability under the normal curve.
Find the area under a normal distribution curve that lies within one standard deviation of the mean is approximattely?
The area under N(0,1) from -1 to 1 = 0.6826
The total area under a normal distribution is infinite?
The total area under a normal distribution is not infinite. The total area under a normal distribution is a continuous value between any 2 given values. The function of a normal distribution is actually defined such that it must have a fixed value. For the "standard normal distribution" where μ=0 and σ=1, the area under the curve is equal to 1.
What is the area under the standard normal distribution curve between z1.50 and z2.50?
~0.0606
What is the area under the standard normal distribution curve between z0.75 and z1.89?
0.1972
What is the significance of the constant 1/sqrt(2pi) in the formula for the standard normal distribution?
The constant 1/sqrt(2pi) in the formula for the standard normal distribution is significant because it normalizes the distribution so that the total area under the curve equals 1. This ensures that the probabilities calculated from the distribution are accurate and meaningful.
Are these true of normal probability distribution IIt is symmetric about the mean TTotal area under the normal distribution curve is equal to 1 DDistribution is totally described by two quantities?
Yes, it is true; and the 2 quantities that describe a normal distribution are mean and standard deviation.
What is the area under standard normal distribution curve between z equals 0 and z equals 2.16?
0.4846
Why does a researcher want to go from a normal distribution to a standard normal distributio?
A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.
What is the area under standard normal distribution curve between z equals 0 and z equals -2.16?
2.16
Why is only one normal table need to find any probability under the normal curve?
A normal distribution is defined by its mean and standard deviation, which are sufficient to describe the entire curve. Once you know these two parameters, you can use the standard normal table (Z-table) to find probabilities for any normal distribution by standardizing values. This process involves converting any normal variable to a standard score (Z-score), which allows you to utilize the same table for all normal distributions. Therefore, only one normal table is needed for any probability under the normal curve.
The distribution of sample means is not always a normal distribution Under what circumstances will the distribution of sample means not be normal?
The distribution of sample means will not be normal if the number of samples does not reach 30.
He area under the standard normal curve is?
The area under the standard normal curve is 1.
Is the area under the standard normal distribution to the left of z equals 0 negative?
The Z value is negative, but area is always positive.
