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Tall girls Refer to Exercise 10.

(a) Make a graph of the population distribution.

(b) Sketch a possible graph of the distribution of sample data for the SRS of size 20 taken by the AP Statistics class.

Short Answer

Expert verified

a). A graph of the population distribution is

b). A possible graph of the distribution of sample data is

Step by step solution

01

Part (a) Step 1: Given Information 

Tall girls:

02

Part (a) Step 2: Explanation 

The population distribution is given to be N(64,2.5), which means a normal distribution with mean 64and standard deviation 2.5.

=64

=2.5

A general normal distribution with mean and standard deviation is of the form:

03

Part (a) Step 3: Explanation 

The graph of the population distribution is

04

Part (b) Step 1: Given Information 

Tall girls:

20individuals are in the sample

We also know that approximately

=64

=2.5

05

Part (b) Step 2: Explanation 

The width of all bars should be equal and the height should be equal to the number of students.

The bars should be roughly centered about 64and the range of values should be within 2standard deviations of the mean.

06

Part (b) Step 3: Explanation

Dot plot:

Draw a number line and place dots above the corresponding numbers which should be centered at about 64and the range of values should be within 2standard deviations of the mean.

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Most popular questions from this chapter

Bad carpet The number of 铿俛ws per square yard is a type of carpet material that varies with mean 1.6铿俛ws per square yard and standard deviation 1.2铿俛ws per square yard. The population distribution cannot be Normal, because a count takes only whole-number values. An inspector studies 200square yards of the material records the number of 铿俛ws found in each square yard, and calculates x, the mean number of 铿俛ws per square yard inspected. Find the probability that the mean number of 铿俛ws exceeds 2 per square yard. Follow the four-step process.

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5,but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation0.7.

(a) What are the mean and standard deviation of the average number of moths xin50traps?

(b) Use the central limit theorem to help you find the probability that the average number of moths in 50traps is greater than0.6.

You want to take an SRS 50of the 816students who live in a dormitory on a college campus. You label the students 001to 816in alphabetical order. In the table of random digits, you read the entries

95592 94007 69769 33547 72450 16632 81194 14873

The first three students in your sample have labels

(a) 955,929,400

(b) 400,769,769

(c) 559,294,007

(d) 929,400,769

(e) 400,769,335

In the language of government statistics, you are 鈥渋n the labor force鈥 if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged 25years and over in a recent year. The table entries are counted by thousands of people.

Unemployment (5.1) What is the probability that a randomly chosen person 25 years of age or older is in the labor force? Show your work.

(a) Sketch a possible graph of the distribution of sample data for an SRS of size 5 with a range of 1000grams.

(b) Explain why the dotplot of sample ranges above is not the actual sampling distribution of the sample range.

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