Questions: Question Lexie averages 149 points per bowling game with a standard deviation of 14 points. Suppose Lexie's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X ~ N(149,14). If necessary, round to three decimal places. Provide your answer below: Suppose Lexie scores 186 points in the game on Tuesday. The z-score when x=186 is . The mean is . This z-score tells you that x=186 is standard deviations to the right of the mean.

Question Lexie averages 149 points per bowling game with a standard deviation of 14 points. Suppose Lexie's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X ~ N(149,14). If necessary, round to three decimal places. Provide your answer below: Suppose Lexie scores 186 points in the game on Tuesday. The z-score when x=186 is . The mean is . This z-score tells you that x=186 is standard deviations to the right of the mean.
Transcript text: Question Lexie averages 149 points per bowling game with a standard deviation of 14 points. Suppose Lexie's points per bowling game are normally distributed. Let $X=$ the number of points per bowling game. Then $X \sim N(149,14)$. If necessary, round to three decimal places. Provide your answer below: Suppose Lexie scores 186 points in the game on Tuesday. The $z$-score when $x=186$ is $\square$ . The mean is $\square$ . This $z$-score tells you that $x=186$ is $\square$ standard deviations to the right of the mean. FEEDBACK MORE INSTRUCTION SUBMIT
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Solution

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Solution Steps

Step 1: Calculate the Z-Score

To find the z-score for Lexie's score of \( x = 186 \), we use the formula:

\[ z = \frac{X - \mu}{\sigma} \]

Substituting the values:

\[ z = \frac{186 - 149}{14} = \frac{37}{14} \approx 2.643 \]

Step 2: Identify the Mean

The mean of Lexie's bowling scores is given as:

\[ \mu = 149 \]

Step 3: Interpret the Z-Score

The calculated z-score indicates how many standard deviations the score of \( x = 186 \) is from the mean. Since \( z \approx 2.643 \), we conclude that:

\[ x = 186 \text{ is approximately } 2.643 \text{ standard deviations to the right of the mean.} \]

Final Answer

The z-score when \( x = 186 \) is \( 2.643 \). The mean is \( 149 \). This z-score tells you that \( x = 186 \) is \( 2.643 \) standard deviations to the right of the mean.

\[ \boxed{z = 2.643, \mu = 149} \]

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