Exam 5: Approximating With a Distribution

Use the following Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 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 There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. The n_m = 13 male students watched an average of 6 hours of television per week with standard deviation 4.24 hours. The n_f = 11 female students watched an average of 3.91 hours of televion per week with a standard deviation of 3.48 hours. Assume that the students enrolled in the statistics class are representative of all students at the university. -The standard error of the differences 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 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 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 Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches. -Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Use the following A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds. -The symmetric middle 90% of songs have lengths between what two values? Round all values to one decimal place.

Use the following A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds. -Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Use the following 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 above a 94% are assigned an "A". What proportion of students earned A's? Report your answer with three decimal places.

Use the following Find the p-value based on a standard normal distribution for the standardized test statistic and provided alternative hypothesis. -z = 2.36 for

Use the following 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? Numerically justify your answer.

Use the following Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches. -The tallest 15% of 10-year-old girls are taller than what height? Report your answer with one decimal place.

Use the following Find the endpoint(s) on a N(0, 1) density with the given property. -The area to the right of the endpoint is about 0.45.

Use the following Select the answer closest to the specified areas for a normal density. -The area to the right of 12 on a N(9.4, 1.2) distribution.

Use the following 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 A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds. -What proportion of songs are between 240 and 360 seconds (4 minutes and 6 minutes)? Report your answer with three decimal places.

Use the following Find the endpoint(s) on the normal density curve with the given property. -The area to the left of the endpoint on a N(25, 3) curve is about 0.1.

Use the following A set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution are provided. Find the value of the standardized z-test statistic. -Test versus when the sample has n = 75, = 25.5, s = 5.4, and SE = 0.6.

Use the following 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 beds that the university currently purchases are 75 inches long. What proportion of males will be able to fit on the bed while lying perfectly straight? Round your answer to three decimal places.

Use the following 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. -Draw a sketch of the distribution of men's heights and label at least three points on the horizontal axis.

In an August 2012 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. Use the normal distribution to test if the proportion of U.S. adults who are dissatisfied with the education that students receive in kindergarten through grade 12 differs from 50%. The randomization distribution for this test is approximately normal and the standard error is SE = 0.016. Include all details of the test and use a 5% significance level.