Question

consider the standard normal curve given.

the mean is dropdown.

the standard deviation is dropdown.

the data point 37 is dropdown one standard deviation from the mean.

Explanation:

Identify the mean

The mean of a normal distribution is located at the center of symmetry of the bell curve. Looking at the horizontal axis, the peak of the curve is centered directly above the value \(30\). Therefore, the mean \(\mu\) is \(30\).

Identify the standard deviation

The standard deviation is explicitly given in the box below the horizontal axis as \(\sigma = 5\). This is also consistent with the axis markings, which increase and decrease by increments of \(5\) (e.g., \(20, 25, 30, 35, 40\)). Therefore, the standard deviation is \(5\).

Calculate the distance in standard deviations

To find how many standard deviations the data point \(37\) is from the mean, we calculate its z-score:

$$ z = \frac{x - \mu}{\sigma} = \frac{37 - 30}{5} = \frac{7}{5} = 1.4 $$

Thus, the data point \(37\) is \(1.4\) standard deviations from the mean.

Answer:

Consider the standard normal curve given.

The mean is <blank>30</blank>.

The standard deviation is <blank>5</blank>.

The data point 37 is <blank>1.4</blank> one standard deviation from the mean.