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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 渭=64inches and standard deviation 蟽=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,

渭=64蟽=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,

渭-3蟽=64-3(2.5)=56.5渭-2蟽=64-2(2.5)=59渭-蟽=64-(2.5)=61.5渭+蟽=64+(2.5)=66.5渭+2蟽=64+2(2.5)=69渭+3蟽=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 渭=64inches.

Standard deviation 蟽=2.5inches.

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

渭-3蟽=64-3(2.5)=56.5渭+3蟽=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

According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home. Which one of the following represents the approximate probability of obtaining a sample of 100 adults in which 65 or fewer own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

a. (10065)(0.71)65(0.29)3510065(0.71)65(0.29)35

b. (10065)(0.29)65(0.71)3510065(0.29)65(0.71)35

c.

P(z鈮�0.65-0.71(0.71)(0.29)100)Pz鈮�0.65-0.71(0.71)(0.29)100

d.P(z鈮�0.65-0.71(0.65)(0.35)100)Pz鈮�0.65-0.71(0.65)(0.35)100

e.P(z鈮�0.65-0.71(0.71)(0.29)100)Pz鈮�0.65-0.71(0.71)(0.29)100

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