Questions: Choose the appropriate term for each definition below. - a bell-shaped probability density curve that (1) has the peak at 0; (2) symmetric about 0; (3) extends indefinitely in both directions, approaching but never touching the horizontal axis; (4) the empirical rule holds - a technique used to approximate the probabilities of a binomial random variable using the normal random variable with the same parameters O a bell-shaped probability density curve that (1) has the peak at μ; (2) symmetric about μ; (3) extends indefinitely in both directions, approaching but never touching the horizontal axis; (4) empirical rule holds O a curve that (1) is always on or above the horizontal axis; (2) has the total area between itself and the horizontal axis equal to 1 standard normal probability density curve O a continuous random variable that has the

Choose the appropriate term for each definition below.
- a bell-shaped probability density curve that (1) has the peak at 0; (2) symmetric about 0; (3) extends indefinitely in both directions, approaching but never touching the horizontal axis; (4) the empirical rule holds
- a technique used to approximate the probabilities of a binomial random variable using the normal random variable with the same parameters

O a bell-shaped probability density curve that (1) has the peak at μ; (2) symmetric about μ; (3) extends indefinitely in both directions, approaching but never touching the horizontal axis; (4) empirical rule holds

O a curve that (1) is always on or above the horizontal axis; (2) has the total area between itself and the horizontal axis equal to 1 standard normal probability density curve
O a continuous random variable that has the

Transcript text: Choose the appropriate term for each definition below. - a bell-shaped probability density curve that (1) has the peak at 0 ; (2) symmetric about 0; (3) extends indefinitely in both directions, approaching but never touching the horizontal axis; (4) the empirical rule holds - a technique used to approximate the probabilities of a binomial random variable using the normal random variable with the same parameters O a bell-shaped probability density curve that (1) has the peak at $\mu$; (2) symmetric about $\mu$; (3) extends indefinitely in both directions, approaching but never touching the horizontal axis; (4) empirical rule holds O a curve that (1) is always on or above the horizontal axis; (2) has the total area between itself and the horizontal axis equal to 1 standard normal probability density curve O a continuous random variable that has the

Solution

Solution Steps

Step 1: Identify the First Definition

The first definition describes a bell-shaped probability density curve that:

Has the peak at $0$
Is symmetric about $0$
Extends indefinitely in both directions, approaching but never touching the horizontal axis
The empirical rule holds

This definition corresponds to the standard normal probability density curve.

Step 2: Identify the Second Definition

The second definition refers to a technique used to approximate the probabilities of a binomial random variable using the normal random variable with the same parameters. This is known as the normal approximation to the binomial distribution.

Step 3: Identify the Third Definition

The third definition describes a bell-shaped probability density curve that:

Has the peak at $\mu$
Is symmetric about $\mu$
Extends indefinitely in both directions, approaching but never touching the horizontal axis
The empirical rule holds

This definition corresponds to the normal probability density curve.

Final Answer

For the first definition: standard normal probability density curve
For the second definition: normal approximation to the binomial distribution
For the third definition: normal probability density curve

Thus, the answers are:

First definition: $\boxed{\text{standard normal probability density curve}}$
Second definition: $\boxed{\text{normal approximation to the binomial distribution}}$
Third definition: $\boxed{\text{normal probability density curve}}$

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