Vacation Expenses Analysis and Z-scores Computation
Explore the concept of measuring dispersion using standard deviation units and calculating z-scores for a dataset related to vacation expenses. Learn how to interpret z-scores, analyze normal distributions, and apply statistical concepts to real-world scenarios involving amusement park trip heights. Discover the importance of graphical representation in understanding frequency distributions.
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1-4 Vacation Expenses OBJECTIVES Measure dispersion using standard deviation units. Compute z-scores. Find percentages using the normal curve. Compute raw scores using z-scores. Slide 1
Key Terms raw data normal curve standard score z-score normal distribution bell curve asymptomatic tails Slide 2
How can graphs help describe frequency distributions? What would help you organize data in a more visual format? Slide 3
Example 1 A summer camp is taking their 220 sixth graders on a trip to an amusement park. For safety purposes, some of the rides have height requirements. The campers heights have a mean of 56 inches and a standard deviation of 3 inches. What is the z-score for a camper with a height of 62 inches? Slide 4
Example 1 A summer camp is taking their 220 sixth graders on a trip to an amusement park. For safety purposes, some of the rides have height requirements. The campers heights have a mean of 56 inches and a standard deviation of 3 inches. What is the z-score for a camper with a height of 62 inches? Slide 5
Example 2 The height of a certain student on this trip had a z-score of -0.5. What is the student s height in inches? Slide 6
Example 2 The height of a certain student on this trip had a z-score of -0.5. What is the student s height in inches? Slide 7
Example 2 The height of a certain student on this trip had a z-score of -0.5. What is the student s height in inches? Slide 8
Example 3 Recall the amusement park trip from Examples 1 and 2. A certain ride requires riders to be at least 51 inches tall. The heights are normally distributed with mean 56 and standard deviation 3. Approximately how many of the camp s 220 sixth graders will not be allowed on the ride? Slide 9
Example 3 Recall the amusement park trip from Examples 1 and 2. A certain ride requires riders to be at least 51 inches tall. The heights are normally distributed with mean 56 and standard deviation 3. Approximately how many of the camp s 220 sixth graders will not be allowed on the ride? Slide 10
Example 3 Recall the amusement park trip from Examples 1 and 2. A certain ride requires riders to be at least 51 inches tall. The heights are normally distributed with mean 56 and standard deviation 3. Approximately how many of the camp s 220 sixth graders will not be allowed on the ride? Slide 11
Example 4 The families of students at Smithtown High School were surveyed about their vacation expenses. The results were normally distributed with mean $2,313 and standard deviation $390. What percent of the families took vacations that cost between $2,000 and $3,000? Slide 12
Example 4 The families of students at Smithtown High School were surveyed about their vacation expenses. The results were normally distributed with mean $2,313 and standard deviation $390. What percent of the families took vacations that cost between $2,000 and $3,000? Slide 13
Example 4 The families of students at Smithtown High School were surveyed about their vacation expenses. The results were normally distributed with mean $2,313 and standard deviation $390. What percent of the families took vacations that cost between $2,000 and $3,000? Slide 14
Example 4 The families of students at Smithtown High School were surveyed about their vacation expenses. The results were normally distributed with mean $2,313 and standard deviation $390. What percent of the families took vacations that cost between $2,000 and $3,000? Slide 15
Example 5 A local travel magazine rates hotels using integers from 0 to 100. Last year they rated over 2,000 hotels. The ratings were normally distributed with mean 78 and standard deviation 6.5. How high would a hotel s rating have to be for it to be considered in the top 10% of rated hotels? Slide 16
Example 5 A local travel magazine rates hotels using integers from 0 to 100. Last year they rated over 2,000 hotels. The ratings were normally distributed with mean 78 and standard deviation 6.5. How high would a hotel s rating have to be for it to be considered in the top 10% of rated hotels? invNorm(.90,0,1) 1.28 Slide 17
Example 5 A local travel magazine rates hotels using integers from 0 to 100. Last year they rated over 2,000 hotels. The ratings were normally distributed with mean 78 and standard deviation 6.5. How high would a hotel s rating have to be for it to be considered in the top 10% of rated hotels? invNorm(.90,0,1) 1.28 Slide 18
