Exam 7: Probability

The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?

Which of the following could possibly be density functions? Select all that apply.

Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. In terms of b (see the graph), find the fraction of the population that is between 60 and 100 years old.

The number of hours of sleep per night averaged by a group of students is approximately normally distributed with mean and standard deviation . What is the probability that a student selected at random had more than 7.5 hours of sleep? Round to 2 decimal places.

The life expectancy of a bug can be approximated by the density function , where t is time in days. Find the probability that a bug lives between 3 and 5 days. Round to 2 decimal places.

The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. What is the probability that the circuit board will cost less than $2 thousand to produce?

The heights, in inches, of flowers in a garden have the density function shown in the following figure. How many inches tall is the tallest flower?

The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10.

Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. According to this simplified model of the distribution of people's ages in the United States, what percentage of the population is between 0 and 100 years old?

The distribution of heights, x, in meters, of a group of shrubs is represented by the density function (no shrubs are higher than 1.5 meters). Calculate the percentage of shrubs which are between 1 and 1.5 meter(s) high.

According to data from 2007, the height of five-year-old girls is normally distributed with a mean of 42 inches and a standard deviation of 1.5 inches. Use your calculator or computer to find the percentage of 5-year-old girls between 43 and 44 inches.

Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What was the median number of credit hours taken by the students?

The final exam scores for a calculus course were approximately normally distributed with mean and standard deviation . The maximum possible score was 100. What is the probability that a randomly selected student received an A grade (90 or higher)? Round to 3 decimal places.

Which of the following could possibly be cumulative distribution functions? Select all that apply.

A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by . Use a calculator or computer to find the median time of emergence.

The heights, in inches, of flowers in a garden have the density function shown in the following figure. The median height is

The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. About what percent of the people in the school are adults? I. II.

A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: What percent of the students would you expect to score below 25 points on the exam?

Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community? I. II. III.

An aptitude test is given to a group of students. Scores can range from 0 to 50. Does the cumulative distribution function in the second graph correspond to the density function in the first graph? Answer "yes" or "no"