a. What is the distribution of X? X~ N( b. Find the proportion of her laps that are completed between 130.02 and 131.67 seconds. c. The fastest 3% of laps are under seconds.

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**Terri Vogel's Lap Time Analysis**

Terri Vogel, an amateur motorcycle racer, averages 129.93 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.25 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible.

a. **What is the distribution of X?**  
   \(X \sim N(\, \underline{\hspace{1.5cm}} \, , \, \underline{\hspace{1.5cm}} \,)\)

b. **Find the proportion of her laps that are completed between 130.02 and 131.67 seconds.**  
   \(\underline{\hspace{4cm}}\)

c. **The fastest 3% of laps are under** \(\underline{\hspace{2cm}}\) **seconds.**

d. **The middle 70% of her laps are from** \(\underline{\hspace{2cm}}\) **seconds to** \(\underline{\hspace{2cm}}\) **seconds.**
Transcribed Image Text:**Terri Vogel's Lap Time Analysis** Terri Vogel, an amateur motorcycle racer, averages 129.93 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.25 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible. a. **What is the distribution of X?** \(X \sim N(\, \underline{\hspace{1.5cm}} \, , \, \underline{\hspace{1.5cm}} \,)\) b. **Find the proportion of her laps that are completed between 130.02 and 131.67 seconds.** \(\underline{\hspace{4cm}}\) c. **The fastest 3% of laps are under** \(\underline{\hspace{2cm}}\) **seconds.** d. **The middle 70% of her laps are from** \(\underline{\hspace{2cm}}\) **seconds to** \(\underline{\hspace{2cm}}\) **seconds.**
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The middle 70% of her laps are from seconds to seconds

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