$30$ . A photographer wants to buy a new camera to take pictures at a sporting event. The table shows the prices of several cameras. The photographer is considering a camera with a price that is within one standard deviation of the mean price. How many of the cameras meet this condition? $\newline$ (A) $5$ cameras $\newline$ \begin{tabular}{|l|l|} $\newline$ \hline \multicolumn{ $2$ }{|c|}{ Camera Prices } \\ $\newline$ \hline $\$ 1200$ & $\$ 1400$ \\ $\newline$ \hline $\$ 2300$ & $\$ 1500$ \\ $\newline$ \hline $\$ 1800$ & $\$ 2000$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ (B) $4$ cameras $\newline$ (C) $2$ cameras $\newline$ (D) $1$ cameras

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Algebra 2

Interpret confidence intervals for population means

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30

. A photographer wants to buy a new camera to take pictures at a sporting event. The table shows the prices of several cameras. The photographer is considering a camera with a price that is within one standard deviation of the mean price. How many of the cameras meet this condition?

\newline

(A)

5

cameras

\newline

\begin{tabular}{|l|l|}

\newline

\hline \multicolumn{

2

}{|c|}{ Camera Prices } \\

\newline

\hline

\$ 1200

\$ 1400

\newline

\hline

\$ 2300

\$ 1500

\newline

\hline

\$ 1800

\$ 2000

\newline

\hline

\newline

\end{tabular}

\newline

(B)

4

cameras

\newline

(C)

2

cameras

\newline

(D)

1

cameras

Calculate Mean Price: Calculate the mean price of the cameras. $\newline$ Mean = $(1200 + 1400 + 2300 + 1500 + 1800 + 2000) / 6$ $\newline$ Mean = $9400 / 6$ $\newline$ Mean = $1566.67$
Calculate Deviations from Mean: Calculate the deviations from the mean for each price. $\newline$ Deviations: $\newline$ $1200 - 1566.67 = -366.67$ $\newline$ $1400 - 1566.67 = -166.67$ $\newline$ $2300 - 1566.67 = 733.33$ $\newline$ $1500 - 1566.67 = -66.67$ $\newline$ $1800 - 1566.67 = 233.33$ $\newline$ $2000 - 1566.67 = 433.33$
Square Deviations: Square each deviation to find the squared deviations. $\newline$ Squared deviations: $\newline$ $(-366.67)^2 = 134444.89$ $\newline$ $(-166.67)^2 = 27777.78$ $\newline$ $733.33^2 = 537777.78$ $\newline$ $(-66.67)^2 = 4444.44$ $\newline$ $233.33^2 = 54444.44$ $\newline$ $433.33^2 = 187777.78$
Calculate Variance: Calculate the mean of the squared deviations (variance). $\newline$ Variance = $\frac{134444.89 + 27777.78 + 537777.78 + 4444.44 + 54444.44 + 187777.78}{6}$ $\newline$ Variance = $\frac{940667.11}{6}$ $\newline$ Variance = $156777.85$
Calculate Standard Deviation: Calculate the standard deviation. $\newline$ Standard Deviation = $\sqrt{156777.85}$ $\newline$ Standard Deviation = $395.95$
Determine Range: Determine the range within one standard deviation of the mean. $\newline$ Lower bound = Mean - Standard Deviation $\newline$ Lower bound = $1566.67 - 395.95$ $\newline$ Lower bound = $1170.72$ $\newline$ Upper bound = Mean + Standard Deviation $\newline$ Upper bound = $1566.67 + 395.95$ $\newline$ Upper bound = $1962.62$
Count Prices in Range: Count how many camera prices fall within this range. $\newline$ Prices within range: $1200$ , $1400$ , $1500$ , $1800$ $\newline$ Count = $4$