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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

Social scientists are interested in the association between the high school graduation rate (HSGR) and the percentage of U.S. families living in poverty (POV). Data were collected from all 50states and the District of Columbia, and a regression analysis was conducted. The resulting least-squares regression line is given by POV=59.2-0.620(HSGR) with r2=0.802. Based on the information, which of the following is the best interpretation for the slope of the least-squares regression line?

(a) For each 1%increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately 0.896.

(b) For each 1%increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately 0.802.

(c) For each 1%increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately 0.620.

(d) For each1%increase in the percentage of families living in poverty, the graduation rate is predicted to increase by approximately 0.802.

(e) For each 1%increase in the per cent of families living in poverty, the graduation rate is predicted to decrease by approximately0.620.

The sampling distribution of p^ is approximately Normal because

(a) there are at least 7570 Division I college athletes.

(b) np=225 and n(1-p)=525.

(c) a random sample was chosen.

(d) a large sample size like n=750 guarantees it.

(e) the sampling distribution of p^ always has this shape.

Your mail-order company advertises that it ships 90%of its orders within three working days. You select an SRS of 100of the 5000orders received in the past week for an audit. The audit reveals that 86of these orders were shipped on time.

(a) If the company really ships 90%of its orders on time, what is the probability that the proportion in an SRS of 100orders is as small as the proportion in your sample or smaller? Follow the four-step process.

(b) A critic says, 鈥淎ha! You claim 90%, but in your sample, the on-time percentage is lower than that. So the 90%claim is wrong.鈥 Explain in simple language why your probability calculation in (a) shows that the result of the sample does not refute the 90%claim.

Suppose we roll a fair die four times. The probability that a 6occurs on exactly one of the rolls is

(a) 4163561

(b) 4161563

(c) 6161563

(d) 163561

(e)161563

Do you drink the cereal milk? A USA Today Poll asked a random sample of 1012 U.S. adults what they do with the milk in the bowl after they have eaten the cereal. Of the respondents, 67% said that they drink it. Suppose that 70% of U.S. adults actually drink the cereal milk. Let p^ be the proportion of people in the sample who drink the cereal milk.

(a) What is the mean of the sampling distribution of p^ ? Why?

(b) Find the standard deviation of the sampling distribution of p^. Check to see if the 10% condition is met.

(c) Is the sampling distribution of p^ approximately Normal? Check to see if the Normal condition is met.

(d) Find the probability of obtaining a sample of 1012 adults in which 67% or fewer say they drink the cereal milk. Do you have any doubts about the result of this poll?

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