BackFinding Specified Data Values In Exercises 31–38, answer the questions about the specified normal distribution.
Weights of Teenagers In a survey of 18-year old males, the mean weight was 166.7 pounds with a standard deviation of 49.3 pounds. (Adapted from National Center for Health Statistics)
c. What weight represents the first quartile?
Finding Specified Data Values In Exercises 31–38, answer the questions about the specified normal distribution.
COVID-19 Response Surveyors asked respondents to rate ten key aspects of their government’s response to the COVID-19 pandemic, including preparedness, communication, and material aid. A pandemic response score that ranged from 0 to 100 was calculated. The mean score for U.S. respondents was 50.6 with a standard deviation of 29.0. (Source: PLOS One)
b. What score represents the 61st percentile?
Finding Specified Data Values In Exercises 31–38, answer the questions about the specified normal distribution.
Billboard Hot 100 The length (in seconds) of the 100 most popular songs during the week of May 5, 2021, can be approximated by a normal distribution, as shown in the figure. (Source: Spotify)
b. What song length represents the 17th percentile?
In Exercises 6–11, find the indicated area under the standard normal curve. If convenient, use technology to find the area.
To the left of z = 0.72
In Exercises 6–11, find the indicated area under the standard normal curve. If convenient, use technology to find the area.
Between z = 0 and z = 2.95
The life spans of car batteries are normally distributed, with a mean of 44 months and a standard deviation of 5 months.
c. What is the shortest life expectancy a car battery can have and still be in the top 5% of life expectancies?
In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. Use this information in Exercises 3–10. (Adapted from 123test)
What is the highest score that would still place a person in the bottom 10% of the scores?
Find each probability using the standard normal distribution.
b. P(z < 2.23)
The random variable x is normally distributed with the given parameters. Find each probability.
c. μ = 5.5, σ ≈ 0.08, P(5.36 < x < 5.64)
Finding Probability In Exercises 41–46, find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability.
Finding Probability In Exercises 41–46, find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability.
Writing Draw a normal curve with a mean of 450 and a standard deviation of 50. Describe how you constructed the curve and discuss its features.
Finding Specified Data Values In Exercises 31–38, answer the questions about the specified normal distribution.
Advanced Dental Admission Test The Advanced Dental Admission Test (ADAT) is designed so that the scores fit a normal distribution, as shown in the figure. (Source: American Dental Association)
b. Between what two values does the middle 50% of the ADAT scores lie?
Finding Specified Data Values In Exercises 31–38, answer the questions about the specified normal distribution.
Red Blood Cell Count The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.4 million cells per microliter and a standard deviation of 0.4 million cells per microliter.
a. What is the minimum red blood cell count that can be in the top 25% of counts?
Bags of Baby Carrots The weights of bags of baby carrots are normally distributed, with a mean of 32 ounces and a standard deviation of 0.36 ounce. Bags in the upper 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be repackaged?