Question

suppose the monthly charges for cell phone plans are normally distributed with mean \\( \mu = \\$ 66 \\) and standard deviation \\( \sigma = \\$ 17 \\).
(a) draw a normal curve with the parameters labeled.
(b) shade the region that represents the proportion of plans that charge less than \\( \\$ 49 \\).
(c) suppose the area under the normal curve to the left of \\( x = \\$ 49 \\) is \\( 0.1587 \\). provide an interpretation of this result.

Explanation:

For part (a), a normal curve is symmetric about the mean \(\mu = 66\). The horizontal axis is labeled \(X\) (monthly charges). The curve has the mean \(\mu = 66\) at the center.
For part (b), since we want the proportion of plans that charge less than \(X = 49\), we shade the region to the left of \(X = 49\) under the normal curve.
For part (c), the area under the normal curve to the left of \(X = 49\) is \(0.1587\). This means that approximately \(15.87\%\) of the cell - phone plans have monthly charges less than \(\$49\).

Answer:

(a) Draw a bell - shaped curve (normal curve) with the horizontal axis labeled \(X\). Mark the mean \(\mu = 66\) at the center of the curve.
(b) Shade the region to the left of \(X = 49\) on the normal curve drawn in part (a).
(c) Approximately \(15.87\%\) of cell - phone plans have monthly charges less than \(\$49\).