Exam 5: Approximating With a Distribution

Use the following to answer the questions below: A Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. The bootstrap distribution (based on 5,000 samples) is provided. ‪ -Gallup conducted a survey of 1,015 randomly selected U.S. adults about "Black Friday"shopping. They asked the following question: "As you know, the Friday after Thanksgiving is one of the biggest shopping days of the year. Looking ahead, do you personally plan on shopping on the Friday after Thanksgiving, or not?"Of the 515 men who responded, 16% said "Yes." Of the 500 women who responded, 20% said "Yes." The standard error of the differences in proportions is about Use the normal distribution to test, at the 5% level, if the proportions of men and women who planned to shop on the Friday after Thanksgiving are significantly different. The sample size is large enough to use the normal distribution.

Use the following to answer the questions below: Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%). -In Professor Albert's course, students who earn less than a 60% in the class are assigned a failing grade (F). What proportion of the students earned F's? Report your answer with three decimal places.

‪ -The standard error of the differences and is about SE = 1.667. Use the normal distribution to test, at the 5% level, if male students at this university watch, on average, more television than female students. Include all details of the test.

Use the following to answer the questions below: It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university. -Should the university be concerned that females will not fit in the 75 inch beds?

Use the following to answer the questions below: Select the answer closest to the specified areas for a normal density. Round to three decimal places. -The area to the left of 32 on a N(45, 8) distribution.

Use the following to answer the questions below: In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves. -The area to the right of 50 in a N(40, 8) distribution converted to a standard normal distribution.

Use the following to answer the questions below: Find the endpoint(s) on a N(0, 1) density with the given property. Round to three decimal places. -The area between ±z is about 0.88.

Use the following to answer the questions below: Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean inches and standard deviation of inches. -A parent says her 10-year-old daughter is in the 95th percentile in height. How tall is the girl? Report your answer with one decimal place.

Use the following to answer the questions below: Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean inches and standard deviation of inches. -What proportion of 10-year-old girls have heights between 50 and 55 inches? Report your answer with three decimal places.

Use the following to answer the questions below: A Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. The bootstrap distribution (based on 5,000 samples) is provided. ‪ -A sample of 148 college students reports sleeping an average of 6.85 hours on weeknights. The sample size is large enough to use the normal distribution, and a bootstrap distribution shows that the standard error is Use a normal distribution to construct and interpret a 95% confidence interval for the mean amount of weeknight sleep students get at this university. Use two decimal places in your answer.

Use the following to answer the questions below: Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean inches and standard deviation of inches. -The tallest 15% of 10-year-old girls are taller than what height? Report your answer with one decimal place.

Use the following to answer the questions below: Find the p-value based on a standard normal distribution for the standardized test statistic and provided alternative hypothesis. -z = -1.86 for : p < 0.5

Use the following to answer the questions below: In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves. -The area to the left of 16 for a N(20, 3) distribution converted to a standard normal distribution

Use the following to answer the questions below: Select the answer closest to the specified areas for a N(0, 1) density. Round to three decimal places. -The area outside of the interval z = -2.13 and z = 1.11.

Use the following to answer the questions below: It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university. -The university decides it is too expensive to replace all the beds. Suppose the university has 2,150 beds all of which are 75 inches long. How many beds should they replace? You may assume that only those males taller than 75 inches will receive the longer beds and that females make up half of the population that will need a dorm room bed.

Use the following to answer the questions below: Use the provided density function to choose the best estimate for the proportion of the population found in the specified region. -The percent of the population that is less than 40 is closest to

Use the following to answer the questions below: Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean inches and standard deviation of inches. -Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Use the following to answer the questions below: Find the p-value based on a standard normal distribution for the standardized test statistic and provided alternative hypothesis. -z = 2.36 for : $\mu$ > 86

Use the following to answer the questions below: Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches. -Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Use the following to answer the questions below: Find the z* values based on a standard normal distribution for each of the following. Round to three decimal places. -An 88% confidence interval for a correlation.