The heights of male seniors in high school closely follow a normal distribution N(µ,0) = N(70.43, 2.73), where the units are inches. Some students suspect that the popularity of high school seniors is related to their height. Suppose the top five nominees for Prom King at a certain high school have an average height of 72.1 inches. a) Find a 95% confidence interval for the average height of high school Prom King nominees by assuming that the standard deviation in their individual heights is the same as th of high school seniors. Give the endpoints of the interval to one decimal place. 95% confidence interval in inches: ( b) Find an 80% confidence interval for the average height of high school Prom King nominees by assuming that the standard deviation in their individual heights is the same as that of high school seniors. Give the endpoints of the interval to one decimal place. 80% confidence interval in inches: (

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### Confidence Intervals for Heights of High School Seniors

The heights of male seniors in high school closely follow a normal distribution \( N(\mu, \sigma) = N(70.43, 2.73) \), where the units are inches. Some students suspect that the popularity of high school seniors is related to their height. Suppose the top five nominees for Prom King at a certain high school have an average height of 72.1 inches.

#### a) 95% Confidence Interval
Find a 95% confidence interval for the average height of high school Prom King nominees by assuming that the standard deviation in their individual heights is the same as that of high school seniors. Give the endpoints of the interval to one decimal place.

**95% confidence interval in inches: ( ______ , ______ )**

#### b) 80% Confidence Interval
Find an 80% confidence interval for the average height of high school Prom King nominees by assuming that the standard deviation in their individual heights is the same as that of high school seniors. Give the endpoints of the interval to one decimal place.

**80% confidence interval in inches: ( ______ , ______ )**
Transcribed Image Text:### Confidence Intervals for Heights of High School Seniors The heights of male seniors in high school closely follow a normal distribution \( N(\mu, \sigma) = N(70.43, 2.73) \), where the units are inches. Some students suspect that the popularity of high school seniors is related to their height. Suppose the top five nominees for Prom King at a certain high school have an average height of 72.1 inches. #### a) 95% Confidence Interval Find a 95% confidence interval for the average height of high school Prom King nominees by assuming that the standard deviation in their individual heights is the same as that of high school seniors. Give the endpoints of the interval to one decimal place. **95% confidence interval in inches: ( ______ , ______ )** #### b) 80% Confidence Interval Find an 80% confidence interval for the average height of high school Prom King nominees by assuming that the standard deviation in their individual heights is the same as that of high school seniors. Give the endpoints of the interval to one decimal place. **80% confidence interval in inches: ( ______ , ______ )**
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