Applications of Normal Distributions: Finding Values

In a survey of women in the United States (ages 20-29), the mean height was 64.1 inches with a standard deviation of 2.71 inches. To the nearest tenth of an inch what height represents the 95th percentile?

In a survey of women in the United States (ages 20-29), the mean height was 64.1 inches with a standard deviation of 2.71 inches. To the nearest tenth of an inch, what height represents the first quartile?

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.00 inches. To the nearest tenth of an inch, what height represents the 90th percentile?

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.00 inches. To the nearest tenth of an inch, what height represents the first quartile?

Scores for the California Police Officer Standards and Training test are normally distributed, with a mean of 50 and a standard deviation of 10. An agency will only hire applicants with scores in the top 10%. What is the lowest score you can earn and still be eligible to be hired by the agency?

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CCSS.HSS.ID.A.4

Scores for the California Police Officer Standards and Training test are normally distributed, with a mean of 50 and a standard deviation of 10. Those officers scoring below the 20th percentile are sent to undergo additional

training. What is the minimum score needed to avoid this training?

The length of time employees have worked at a particular company is normally distributed with mean 11.2 years and standard deviation 2.1 years. If the lowest 10% of employees in seniority are to be layed-off in a cutback, what is the maximum length of time that an employee could have worked and still be laid off?

The length of time employees have worked at a particular company is normally distributed with mean 11.2 years and standard deviation 2.1 years. If the highest 10% of employees in seniority are to be promoted, what is the minimum length of time that an employee could have worked and still be promoted?