Warm-Up Algebra 2 Honors 3/25/19

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Warm-Up Algebra 2 Honors 3/25/19 A line of bicycles is designed to accommodate adult women whose height is in the middle 95% of the population. Assume that adult women have a mean height of 5 feet 2 inches, with a standard deviation of 2.8 inches. 1. How many inches tall , to the nearest half-inch, is the tallest woman the bike will accommodate? 5 to do 5 to go over 10 total

z-scores When a set of data values are normally distributed, we can standardize each score by converting it into a z-score. z-scores make it easier to compare data values measured on different scales.

z-scores A z-score reflects how many standard deviations above or below the mean a raw score is. Where x represents an element of the data set, the mean is represented by and standard deviation by .

Example: Analyzing the data Suppose SAT scores among college students are normally distributed with a mean of 500 and a standard deviation of 100. If a student scores a 700, what would be their z-score? Her z-score would be 2 which means her score is two standard deviations above the mean.

Let’s try some: Look at #6 on your packet from last week: How many standard deviations away from the mean is 75? What is the z-score for 75? How many standard deviations away is 65 from the mean? What is the z-score? What about 77? 1 -1 𝒛= 𝟕𝟕−𝟕𝟎 𝟓 = 𝟕 𝟓 =𝟏.𝟒

Think about it The z-score is positive if the data value lies above the mean and negative if the data value lies below the mean.

Analyzing the data A group of data with normal distribution has a mean of 45. If one element of the data is 60, will the z-score be positive or negative? The z-score must be positive since the element of the data set is above the mean.

For which test would a score of 78 have a higher standing? Analyzing the data A set of math test scores has a mean of 70 and a standard deviation of 8. A set of English test scores has a mean of 74 and a standard deviation of 16. For which test would a score of 78 have a higher standing?

To solve: Find the z-score for each test. Analyzing the data A set of math test scores has a mean of 70 and a standard deviation of 8. A set of English test scores has a mean of 74 and a standard deviation of 16. For which test would a score of 78 have a higher standing? To solve: Find the z-score for each test. English 𝑧−score= 78−74 16 =.25 The math score would have the highest standing since it is 1 standard deviation above the mean while the English score is only .25 standard deviation above the mean.

Analyzing the data What will be the miles per gallon for a Toyota Camry when the average mpg is 23, it has a z value of 1.5 and a standard deviation of 2?

The Toyota Camry would be expected to use 26 mpg of gasoline. Analyzing the data What will be the miles per gallon for a Toyota Camry when the average mpg is 23, it has a z value of 1.5 and a standard deviation of 2? Using the formula for z-scores: The Toyota Camry would be expected to use 26 mpg of gasoline.