What does it mean when we say that the tails of a normal curve are asymptotic?

The tails are asymptotic, which means that they approach but never quite meet the horizon (i.e. x-axis). For a perfectly normal distribution the mean, median and mode will be the same value, visually represented by the peak of the curve.

Why normal curve is asymptotic to the x-axis?

Two curves that get closer to each other but never intersects is the example of asymptotic. In the case of normal curve, we can see that the curve is close to x-axis and may infinitely touches the x- axis. Hence, the normal curve is asymptotic to the x-axis.

What does asymptomatic to the x-axis mean?

Asymptotes of functions Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. As the name indicates they are parallel to the x-axis. Vertical asymptotes are vertical lines (perpendicular to the x-axis) near which the function grows without bound.

What is the probability that a normal random variable is less than its mean?

In other words, the probability is 0.01 that the value of a normal variable is lower than 2.33 standard deviations below its mean.

What does it mean to say that the exponential distribution is memoryless?

The exponential distribution is memoryless because the past has no bearing on its future behavior. Every instant is like the beginning of a new random period, which has the same distribution regardless of how much time has already elapsed. The exponential is the only memoryless continuous random variable.

What does it mean to say that the graph of the normal distribution is symmetric?

What is Normal Distribution? Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.

Does a normal curve touch the x-axis?

The curve never touches the x axis. Theoretically, no matter how far in either direction the curve extends, it never meets the x axis—but it gets increasingly closer. The total area under a normal distribution curve is equal to 1.00, or 100\%.

What term defines that the normal curve gets closer and closer to the horizontal axis but never touches it?

Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it.

What is the x-axis in a normal distribution?

Figure 9.6: {The normal distribution with mean mu=0 and standard deviation sigma=1. The x-axis corresponds to the value of some variable, and the y-axis tells us something about how likely we are to observe that value. However, notice that the y-axis is labelled “Probability Density” and not “Probability”.

Can a normal distribution across the x-axis?

Each normal distribution is defined by µ (mean) and σ (standard deviation; σ determines the sharpness or flatness of the curve). Characteristics of the Normal Distribution Curve: (The curve never crosses the x-axis.)

What does it mean to say that the exponential distribution is memoryless quizlet?

What does it mean to say that the exponential distribution is “memoryless”? it has a constant failure rate. The probability distribution of a discrete random variable is called its probability. mass function.