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Chapter 7: Q. 12 (page 455)

Tall girls According to the National Center for Health Statistics, the distribution of height for 16-year-old females is modeled well by a Normal density curve with mean μ=64inches and standard deviation σ=2.5inches. Assume this claim is true for the three hundred 16-year-old females at a large high school.

a. Make a graph of the population distribution.

b. Imagine one possible SRS of size 20from this population. Sketch a dotplot of the distribution of sample data.

Short Answer

Expert verified

Part(a) The graph

Part(b) The dot plot is

Step by step solution

01

Part(a) Step 1 : Given information

We need to draw graph for given data.

02

Part(a) Step 2 : Simplify

As given,

μ=64σ=2.5

Now,

68%lies in first standard deviation from mean.

95%lies in second standard deviation from mean.

99.7%lies in third standard deviation from mean.

Now, from the formula of standard deviation,

μ-3σ=64-3(2.5)=56.5μ-2σ=64-2(2.5)=59μ-σ=64-(2.5)=61.5μ+σ=64+(2.5)=66.5μ+2σ=64+2(2.5)=69μ+3σ=64+3(2.5)=71.5

The graph is

03

Part(b) Step 1 : Given information

We need to draw dotplot for the given data.

04

Part(b) Step 2 : Simplify

As given, Mean μ=64inches.

Standard deviation σ=2.5inches.

SRS size is 20Now, the values that are centered are nearly 64,

μ-3σ=64-3(2.5)=56.5μ+3σ=64+3(2.5)=71.5

The dotplot would be roughly a bell-shaped pattern.

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Most popular questions from this chapter

Sample proportions List all 10possible SRSs of size n=2, calculate the proportion of females for each sample, and display the sampling distribution of the sample proportion on a dotplot.

In a residential neighborhood, the median value of a house is \(200,000. For which of the

following sample sizes is the sample median most likely to be above \)250,000?

(a) n=10n=10

(b) n=50n=50

(c) n=100n=100

(d) n=1000n=1000

(e) Impossible to determine without more information.

AP2.20 A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ( \( 500, \) 100, \(25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Here is the probability distribution of the amount won on a randomly selected ticket:

Which of the following are the mean and standard deviation, respectively, of the winnings?

a. \) 15.00, \( 2900.00

b.\) 15.00, \( 53.85

c. \) 15.00, \( 26.93

d. \) 156.25,\( 53.85

e. \) 156.25, $ 26.93

When people order books from a popular online source, they are shipped in boxes.

Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5 pound with a standard deviation of 0.1 pound, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?

a. 1.84

b. 2.60

c. 3.02

d. 3.40

e. 9.10

The mean of this distribution (don’t try to find it) will be

a. very close to the median.

b. greater than the median.

c. less than the median.

d. You can’t say, because the distribution isn’t symmetric.

e. You can’t say, because the distribution isn’t Normal.
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